How To Solve Y=mx+b
How do you solve and graph a simple y=mx+b equation?
For example: y=5x+6
I don't get how to graph any of it, and I don't get how to add/subtract/multiply/divide any of it.
Hey Shelly,
All of these answers are great, but unless you get a better conceptual understanding of the basic parts of a slope intercept equation you will continue to struggle with these equations in the future. In y=mx+b the two parts that we focus on are m, which represents the slope or slant of the line, and b, which represents the yintercept.
Let's start with b, the yintercept. The yinterceptb, and more specifically the number that will be in the place of b in the actual equation you want to graph, represents a point on the y axis itself. Think of it like an interception in football. The quarterback throws the ball to his player, and the path of the ball is a line from the quarterback to his receiver. To intercept the ball, the defender from the opposing team has to cross that line between the quarterback and his intended receiver. This is like the yintercept, or b, in our equation. It is the exact point where the line you graph will intersect with the y axis, or vertical axis. When your equation is in slope intercept form, or yintercept form if you prefer, you can quickly find that point by simply knowing where to look. First you have to be sure the equation is in slope intercept form, here is a quick guide. You can easily tell if an equation is in slope intercept form by looking for a couple of quick details: first, y has to be all by itself on 1 side of the equal sign; second, the x term will be first on the other side, followed by a constant (a number without a variable) that is being added or subtracted.Consider the following example: actual equation y=2x+3
generic form y=mx+b
Notice how the parts line up. Positive 2 is where the m is located in the generic form, and positive 3 is where the b is in the generic form. That means positive 3 is our yintercept. To locate this on your graph, you simply find the positive 3 on the y axis, which will be up 3 places from the origin of the graph, or where the x and y axis intersect one another. Put a dot there where you found the y intercept. If the number in place of b were negative, say 3, then you would simply go down on the y axis 3 spaces from the origin. Try looking at a few different slope intercept equations and just spot the y intercepts to get familiar and comfortable with this step, then proceed to the next part: Slope.
The 2 in our example represents the m, or slope of the line. Slope is rise over run, or change in y over change in x. More simply though, it is the slant of the line. Is the line steep, does it rise quickly, or is the line more flat? It is easier for us to use slope in the form of a fraction, so first let's change the 2 into its equivalent fraction, 2/1. 2/1 represents a rise of two (how far you go straight up from your yintercept), and a run of 1(how far you move left or right from your y intercept). If your slope is positive, you will count up and then to the right(or inversely down and to the left). If your slope is negative you will count up and to the left(or inversely down and to the right). Our slope is positive, so starting from your yintercept of 3 you will count up 2 times, and then to the right 1 time. That should put you at the coordinates (5,1). Plot this point by putting a dot there, and then simply connect that point to your yintercept point with a straight line. If you run out of room on your graph counting up for your slope, start over at your yintercept and go down 2 and to the left 1. I hope this helps. Good Luck
The first thing to do when looking at this problem is to take a close look at the equation y = 5x +6. This equation is in what is called "slope intercept form." Slope intercept form is y = mx + b. (This format is something you should remember.) The letter "m" is the "slope" of the equation and the "b" is the "yintercept."
If you were taking a standardized test, such as the ACT, that has multiple choices, I would have you approach the problem in this way as it may possibly save you time. I would first look at the slope. The slope of this equation is 5 which is positive. Slope tells us in which direction the line will go and how steep it is. Since the slope in this equation is positive, it means that a person would walk up the hill for this equation. (The line would start lower on the left and look like a hill going up to the right.) At this point, I would look at the multiple choice answers and it may be possible to pick the graph out with just this information (i.e. Which one(s) are going uphill?). If not, it is usually possible, to at least eliminate a couple of "bad" answers.
The next step would be to look at the "yintercept." This is the point where the line crosses the yaxis (up and down axis). So, back to taking a standardized test, look at the answers and find the choices that go "uphill" and go through (the line touches) the point (0. 6). This will usually be enough information to get your answer.
If you are not taking a multiple choice test and have to actually graph this equation, you should do the following. Start at the yintercept point because you are 100% confident that this point is on the line. So, in this case, go over 0 (the first coordinate always goes right/left) and down 6 (the second coordinate always goes up/down with up being positive and down being negative). Put a point at (0, 6).
The slope of this equation is 5. We always think about the slope as a fraction, however. If there is not a fraction, make one by putting a fraction bar and a 1 under the number. So, our slope would be 5/1. From our point (0, 6) we will go over 1 to the right (bottom of slope is always left/right with positive to the right and negative to the left) and up t (top of slope is always up/down with positive up and negative down). This should get us to point (1, 1). Put a point here.
Now, since you have two points of the line, you have enough to actually create the line. Connect the two points and continue in both directions to the edges of your graph. Remember to put an arrow on each end of the line to indicate that a line continues to infinity.
If you like to have more points to create your line, just continue the process we followed to get to (1, 1). The next point would be (2, 4). This is not really necessary, though.
Graphing a linear equation written in slopeintercept form, y= mx+b is easy! Remember the structure of y=mx+b and that graphing it will always give you a straight line.
**There are MANY ways to graph a linear equation. Using the slope and yintercept (that I am about to show you) is the easiest.**
"b" represents the "yintercept" of the line. This is where the line cross es the yaxis (the part of the coordinate grid that goes up and down).
"m" represents the "slope" of the line. This is rise/run.
Let's say you're given the equation y = 2/3x + 4
The Steps:
1) Always start on the yintercept (the number that is by itself and doesn't have "x" attached to it. If you are not given a yintercept, start at 0. In this case, start by putting a dot on 4 on the yaxis.
2) Look at the slope, or the "m" (many times, it's the fraction. If you are not given a fraction, write the number attached to "x" over 1).
3) Remember that slope represents rise/run. Since my slope is 2/3, I am going to start at the yintercept of 4 and count UP 2 dashes, and OVER 3.
4) Put another dot. Connect the two dots you just plotted with a line that extends throughout the entire coordinate grid.
5) Smile! You've just graphed a linear equation!
You can solve the equation and graph it by the following steps.
y = mx + b y = 5x +6
Determine if the graph is going to be upward or downward by looking at the sign on the m. With the above equation, the 5 is positive. So, the graph is going to point upward.
Identify the slope and intercepts.
With this equation, 5 represents m, which is the slope, and the yintercept is (0,6), which is given by b, OR by plugging 0 in for x. Then, multiply 5 and 0 and add the 6. The yintercept is (0,6). You would go to 0 on the coordinate plane, and up 6, and plot a point. This is where the graph is going to cross/intersect the yaxis.
The xintercept is calculated/computed when 0 is substituted for y and the opposite of 6, which is 6, is added to both sides; then, divide both sides by 5. So, the xintercept is (6/5,0) (you would go to 6/5,0 and make a point. This is where the graph is going to cross/intersect the xaxis.
To graph the equation, you would plot the x and y intercepts and plot other points using the slope of 5/1 (rise/run). Connect the points.
There are two different ways to graph that equation.
1. You can use the slope and yintercept of the line to graph it. The slope is the number that is in front of x (in your example 5 would be the slope). The slope will tell you the rise and run of the line. (In other words, how far up and over you will go from your yintercept.)Your yintercept is the number that is by itself (in your example, 6). On your graph, go to 6 on the yaxis. The 6 will be 6 down from the origin. Now from that point, use your slope to mark 2 more points. From 6 go up 5 and right 1, mark that point. From your new point, go up 5 and right 1, mark another point. Now you have 3 points to make a line.
2. You can also do a Tchart. You can pick random numbers to use for x. any numbers that you want to use will work fine. I usually use 1, 0, 1. Take your numbers and plug into the equation. For 1, I will do 5(1) + 6 = 11. So that will make a point (1, 11). For 0, I will do 5(0) + 6 = 6. So that will make the point (0, 6). For 1, I will do 5(1) + 6 = 1. That will make the point (1, 1). You have 3 points to make a line now.
Any equation in y=mx+b form is as easy as counting and connecting the dots!
For the equation y=5x+6, you start with the constant. That's the number without the x. In this case, the number is 6. Find that number on the yaxis, and make a dot on it.
Now, you're ready for the slope. That's the number before the x. First, write it as a fraction. Since 5 has no denominator, put a 1 under it. For numbers that already are written as fractions, you don't have to do this step.
Starting with the dot you made on 6, count up (if the 5 were negative, you'd count down) 5 units on the graph. You always count up (+) or down () for the numerator. Then, count over (always go to the right) one. Make a dot where you land.
Now, connect your dots! Extend your line in both directions to the edges of the graph.
So...to summarize: Make a dot on 6 on the yaxis. Starting there, count up 5 units and to the right one unit. Make a dot there. Draw a line that goes from one edge of the graph to the other that passes through your dots! All Done!!
y = mx + b is the slopeintercept form of a line.
"m" is the slope
"b" is the yintercept (the point where your line crosses the yaxis)
In your sample: y = 5x + 6
m = 5 (or 5/1)
b = 6
To graph the line, simply put at point at "6" on the yaxis.
The use the slope of 5 to find the next point (up 5 spaces, over one to the right).
Then sketch the line that passes through these two points.
In your equation y=5x+(6). 5 represents the slop (or steepness) of the line. (6) represents where your line crosses the yaxis (vertical axis) often referred as the yintercept. Therefore, plot your yintercept. From your yintercept count your slope. Since 5 means 5/1, from your yintercept go up (positive 5) 5 and then right (positive) 1. Connect the points and you'll have your graph of your line.
We know the given eqaution y=mx+b represents a straight line with slope m and the y intercept b.
So now let us see how to graph the equation y=5x+(6):
Putting x=0, we get y=6 which implies one coordinate is (0,6)
Now putting x=1, we get y=1 which implies the coordinate is (1,1)
Putting x=2, we get y=4. So the coordinate is (2,4)
Similarly we get coordinates by substituting different values for x.
Finally joining all these coordinate points we get a straight line as shown below:
For any equation in the form y=mx+b, b is the y intercept. The point (0,b) is on the graph. From (0,b) use the slope m to find the next point. m is in the form of a/b where a is the change in y and b is the change in x. Plot the second point and draw a straight line.
You have to note that y=mx+b is a linear equation, so the graph is a straight line.
In order to build the graph, you have to plug in values for x, and find the values for y.
For tracing the line, it's necessary to have two points. That means having 4 coordinates. You know that a point is defined by its coordinate (x,y).
y=5x6
For x = 0
y = 5*0 6
y = 6
The point has the following coordinates: (0,6)
For x = 1
y = 5*(1) 6=56=11
The point has the following coordinates: (1,11)
Now, in order to graph, trace the system of coordinates, which means two rectangular axes. ox is perpendicular to oy. Choose an unit of measure (for example, if you're working on a math sheet, a unit of measure could be the square from the page)
The negative values, on ox axis, are on the left side and the positive values are on the right side. In the middle of the axis is origin, which has coordinates (0,0).
The negative values, on oy axis, are above origin, and negative values are below origin.
For the point (1,11), on ox axis, number 1 square on the left side and, for oy axis, number 11 squares below origin.
y = mx+c. If you give various values for x you obtain corresponding values of y. And plot it , you can confirm that it is a straight line.
You can plot the graph yourself.
The given equation is y=5x6.
Find y values for any x values. Take the easiest values for x and putting it in the equation you get y value.
y = 5x 6 ;
y= 5*06 = 6. y is 6 when x=0.
y=5*16 = 1. Y is 1 when x=1
y=5*26 = 4 . y is 4 when x = 2.
y=5*36 = 9 . y is 9 when x=3.
y=5*46= 14. y is 14 when x= 4.
y=5*56= 19 y is 19 when x= 5
.............
y= 5*156=69. Test whether it is on the graph.
Plot the coordinates: (x,y): (0,6),(1, 1), (2,4) (3,9),(4,14),(5,19). And see whether the point (15,69 ) falls on the graph. Is not the graph a straight line?
Don't get dishartened. You can do well in mathematics.Go through the reference below in maths and follow all the links.
Isn't m the slope and b the y intercept? So can't you just mark (0, 6) on the graph, and then count up 5 and over 1, mark the point (1,1), and draw the line?
Lines are pretty boring but also powerful and very important in your study of mathematics. The basic idea: if you pick any two points on a line and compute the slope, which is "change in y" divided by "change in x", you'll get the same number. ANY two points. No other mathematical shape will have that property.
From this idea comes several forms of the equation of a line. You've asked about the "slopeintercept" form: y = m*x + b.
The "m" stands for "slope" and the "b" is the "yintercept".
Let's talk about the yintercept first. It's called that because it's the yvalue at which the line crosses the yaxis. I.e., the point (0, b) is on the line. Can you see why? Well, let x equal zero. Then y=m*0+b=b, no matter what value "m" has. So yes, the point with x=0 and y=b, called (0,b), is on the line.
Now let's think about slope. Let b=0 and m=2/3 for this conversation. The slope being 2/3 means that if the "change is y" is 2, then the "change in x" must be 3. Let's see that that happens:
Pick any value for x, such as x=5.
Then y=(2/3)*5=10/3.
Let x go up by 3, so x=8.
Now y=(2/3)*8=16/3 so the change in y is (16/3)(10/3)=6/3=2.
With this understanding, you can now graph lines in this form easily:
First graph the point (0,b) since you know that is the yintercept.
Now write the slope as a fraction (perhaps with a denominator of 1). Count "change in y" units up (or down, if that is a negative number) then "change in x" units to the right (or left, if it is a negative number) to get a second point. (You might want to graph three points, just to be sure you're counting correctly.) Then connect the dots!
You should be sure you understand the other form of a line also:
yk=m(xh) which I think is the best, called "pointslope" form.
Easy, this is a linear equation and what you will expect is a straightline graph.
To get the yvalues,
sub x=0
y= 5(0)6
y=6
Mark (0,6) into your graph paper
Then sub. x=1
y=5(1)6
y=1
Mark (1,1) on graph paper.
Do it for more xvalues, then join the points up to form a straightline graph.
y=mx+b is in slope intercept form
m is the slope and b is the y intercept
y = 5x6
_________________________
We need 2 points to graph a line
Our first point will be the on the y axis (the y intercept), x is always 0 on the y axis:
(0, 6). The 6 comes from b
The slope is 5, the m value; which is the same thing as 5/1
5/1 is the rise(up or down)/run(left or right).
From the (0, 6) point get the next point by going up 5, then to the right 1. This is what the 5/1 tells you to do.
Connect the two points
We are talking about solving an equation on an x and y coordinate graph. This graph consist of a horizontal number line called the x axis crossed by a vertical number line called the yaxis. Let's talk about what each term in our equation represents.
y = mx + b
m is the slope (which means rise/run)
b is where our line will cross the yaxis (known as yintercept)
x,y are coordinate points
Example: y = 5x + 6
m = 5 or 5/1 (to express in the form rise/run)
b = 6
Picturing our coordinate plane as two intersecting number lines we determine our line crossed the yaxis at (6) and place a point there. Next we determine our slope to be 5/1 (rise/run). This means we start at our point of the yintercept and rise(go up) 5 units and then run (go out) 1 unit. The final coordinates of this point are (1, 1). After drawing that point we connect our two points with a line. (this is the graph of our equation)
Next we make an x, y chart to determine points which will satisfy our equation. For example: if x = 2, then y = 4. You simply choose a value for x and insert it in your equation to find a value for y.
y=mx+c is called alinear equation in mathematics and is actually the equation to a straight line ie if you put in different values for x and plot the corresponding values of y on a graph the points can be joined to form a straight line
a)To plot any graph with two variables x and y, the easiest way is to substitute some values for x. The best way is to put some basic values for x like 2,1,0,1 and 2
In your example, y=5x+6, we can give the above values for x, one by one
1. when x=2
then y=5*(2)+6 = 10+6 = 16
So the first point to plot is (2,16)
2.When x=2
y=5*2+6 = 10+6 = 4
So the secont point is (2,4)
actually these two points are enough to plot a straight line .
b) To divide/multiply any equation we have to divide /multiply both the left and right side of the equation by the number
eg:
1. y=5x+6 multiplied by 3 will be
3*y=3*(5x+6)
3y = 3*5x + 3*6
3y = 15x +18
2. y=5x +6 divided by 5 becomes
y/5 = (5x+6)/5
y/5 = 5x/5 + 6/5
y/5 = x + 6/5
hope you got it now
the b becvomes your y intercept and is plotted on the graph
then a is your slope
slope ids rise/run
so if a=3 then you would go up 3 and over 1 from your y intercept and continue the line straight
it is general equation of slope intecept
y = mx + k
m = slope
k = intercept
let x = 0
y = 5 ( 0 ) + 6
y = 6
similerly put the value 1 and solve it
y = 5 (1) + 6
y = 11
now plot it on graph
initialy take y on y axis and x on x axis
where x = 0, y = 6
next x= 1, y = 11
increase the straight line as yourequired to upward
it shows that there is positiv erelationship b/w x and y
by the way f(x)=ax+b (linear function or grade I function)
f : R>R
and you have f(x)=5x6
f(x)=y
and x=is a variable (you can give any value)
for example (x=2) from this two => we have A(2,4)
f(x)=5*26 =>y=4
and (x=3) from this two =>we have B(3,9)
f(x)=5*36 =>y=9
now Gf
y
9____________B
 
 
 
 
4_______A 
  
  
  
0_______2____3________________________________ X
and you get AB
First off, let me say that graphing linear inequalites is much easier than your book makes it look. Here's how it works:
Think about how you've done linear inequalites on the number line. For instance, they'd ask you to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing twovariable linear inequalities are very much the same.
 Graph the solution to y < 2x + 3.
Just as for numberline inequalities, my first step is to find the "equals" part. For twovariable linear inequalities, the "equals" part is the graph of the straight line; in this case, that means the "equals" part is the line y = 2x + 3:
Now we're at the point where your book probably gets complicated, with talk of "test points" and such. But when you did those onevariable inequalities (like x < 3), you didn't bother with "test points"; you just shaded one side or the other. We can do the same here. Ignore the "test point" stuff, and look at the original inequality: y < 2x + 3.
I've already graphed the "or equal to" part (it's just the line); now I'm ready to do the "y less than" part. In other words, this is where I need to shade one side of the line or the other. Now think about it: If I need y LESS THAN the line, do I want ABOVE the line, or BELOW? Naturally, I want below the line. So I shade it in:
And that's all there is to it: the side I shaded is the "solution region" they want.
This technique worked because we had y alone on one side of the inequality. Just as with plain old lines, you always want to "solve" the inequality for y on one side.
 Graph the solution to 2x – 3y < 6.

2x – 3y < 6
–3y < –2x + 6
y > ( 2/3 )x – 2
First, I'll solve for y:
[Note the flipped inequality sign in the last line. I mustn't forget to flip the inequality if I multiply or divide through by a negative!] Copyright © Elizabeth Stapel 20002011 All Rights Reserved
Now I need to find the "equals" part, which is the line y = ( 2/3 )x – 2. It looks like this:
But this exercise is what is called a "strict" inequality. That is, it isn't an "or equals to" inequality; it's only "y greater than". When I had strict inequalities on the number line (such as x < 3), I denote this by using a parenthesis (instead of a square bracket) or an open [unfilled] dot (instead of a closed [filled] dot). In the case of these linear inequalities, the notation for a strict inequality is a dashed line. So the border of my solution region actually looks like this:
By using a dashed line, I still know where the border is, but I also know that the border isn't included in the solution. Since this is a "y greater than" inequality, I want to shade above the line, so my solution looks like this:
y=5x+6
y=mx+b
note:"m" is always the number in front of X which is also known as the slope. And "b" is the yintercept. so in this case: m=5, b=6
next is to plot 6 on the yaxis first, then you make 5 to be divided by 1. E.g 5/1. Next when u have plot 6 on the yaxis, from that point, u go up 5 times and move to ur right just once. do it repeatedly. normally the formula is always rise/run, but u have to use the simpler step for now before u become perfect. hope this helped. anyways u're welcome:)
y = 5x 6 ;
y= 5*06 = 6. y is 6 when x=0.
y=5*16 = 1. Y is 1 when x=1
y=5*26 = 4 . y is 4 when x = 2.
y=5*36 = 9 . y is 9 when x=3.
y=5*46= 14. y is 14 when x= 4.
y=5*56= 19 y is 19 when x= 5
OR
y= 5*06 = 6. y is 6 when x=0.
y=5*16 = 1. Y is 1 when x=1
y=5*26 = 4 . y is 4 when x = 2.
y=5*36 = 9 . y is 9 when x=3.
y=5*46= 14. y is 14 when x= 4.
y=5*56= 19 y is 19 when x= 5
y=point on y axis
x=point on x axis
m=gradient of the line (this means wether the line is sloping upwards or downwards) .It goes frm left to right.
step 1.Find th gradient if its not there.This can be done by taking two points on a line in a graph. the formula is {y2y1}÷{x2x1)
step 2.After finding the gradient, the axises can be subbed.
step 3.Using linear equation, b which is the point on the y axis where the line meets it can be found .
step 4.After finding b, u can kick out the values of x and y hence only using the values of m & b.
lord voldermort
:)
well all you have to do is put all the number together then ge ton ask.com and typre in the eqautins and en you do that they would give you the answer to your question then you will get yur answer and can use ot for whatever you needed it for and n 9 timexs ouit of 10 it wikl be right yu just have to look at the one that makes more sense to not one that has many options or sum
It's already in the form it has to be in otehr to graph it.you simply as to go down 6 on the yaxis because it's negative and after that you go up 5 because the slope is 5 and then you move to the right 1.
okay so your problem is y=5x+(6)
You are going to want rewrite it so it is easier to read  y=5x6
you already have the yintercept which is the b in the formula or in this case the 6. and your slope would be the m in the formula on in this case the 5.
to graph it put a point on the ordered pair (0,6), then to get your line you want to go up 5 units from the point (0,6) and 1 unit to the right of that. Then you have graphed your slope intercept form.
To solve it is more easy plug in a point on your line
(1,1), 1=5(1)6
multiply 5 and 1 and you have the equation, 1=56
subtract 5 and 6 and you have the answer, 1=1
y=5x+6
start my placing the 6 on the yaxis. then the slope is 5 or 5/1. so you would go up 5 from the 6 and to the right 1 since it is a positive slope.
y=mx+b
this is yintercept form
M= slope/ rise over run
b= the yintercept
start at the y intercept and then graph the rest of the line using the righ slope.
find when x=0 Y=?
and y=0 X=?
like if y=3x+1
than when x=o, y=1
and y=0, X= 1/3 OR
go to 1 on y and than go 3 rise over 1run,if it has negative sign in it go 3 down over 1run.....
y=mx+b is a linear equation which will cause you to have a straight line. m is the slope of the line (rise/run). The x and y are intercepts found on the graph which are usually given. In order to solve it you simply plug in the numbers leaving one unknown which will be B. One way to find the slope is to find the derivative of the function given (calculus) by doing that you simply plug in the derivative (m) with the x and y. lets say that m = 5 x= 4 and y = 10. You simply do 10 = 20 + then you see that B = 10/20 or 1/2 . So you are left with the function y= 5x + 1/2
so if the equation is y=5x+(6) it can also be rewritten as y=5x6 because when you have a + and  together it will always be a .
a lot of people say to make a table and plug in some numbers but you can just go straight to graphing it. so 6 is the yintercept because it represents b and 5 is the slope. the actual fraction is 5/1 which is in the formula rise over run. so...
1. make a coordinate plane with all 4 quadrants
2. put a point at (0,6)
3. from that point go up 5 units and right 1 then do the same from that
4. connect
5. viola! you made a graph
http://www.khanacademy.org/video/slopeandyinterceptintuition?playlist=Algebra
this gives notes on slope
The only thing you have to know to graph it is the 'm' being the slope so for your equation it is 5 (5/1) and the 'b' which is the y intercept so you would go to the y inter. start at 6 and go up 5 over 1 put a dot and draw a line
y = mx + b is the general form of a linear equation (when it is graphed it is a straight line).
M is the slope, or the steepness, of the line, and b is the yintercept, where the graph crosses the yaxis.
To graph:
1. Rewrite the equation. You have y = 5x+ 6, when you add a negative we are really just subtracting so we can write it as: y = 5x6.
2. Identify the yintercept. Since the yintercept is where the graph crosses the yaxis the xcoordinate will be 0. So, the yintercept is (0,6).
3. Use the slope to find a second point on this line. Write the slope as a fraction so you know how many to go up or down and left or right. The slope is 5 or 5/1, so from the yintercept (0, 6) you go up 5 units and to the right 1 unit. This is the second point on this line.
4. Use a ruler to connect the 2 points. Put arrows on the end to indicate that this is a line and lines go on infinitely.
5. Label the graph. Put the equation y = 5x6 by one of the arrows.
Good luck.
Solve usually refers to finding the x intercept of a graph.
Therefore one simply replaces y with zero
0=5x+6
Now move 6 to the left by using the property of transpose (when moving a number from one side to another, you change its sign)
6=5x
now simply divide by 5
6/5=x
The zero is at (6/5,0). This is because (x,y)
Now to graph this baby
Simply substitute x values with numbers and get y values
y= 5*06 = 6. y is 6 when x=0.
y=5*16 = 1. Y is 1 when x=1
y=5*26 = 4 . y is 4 when x = 2.
y=5*36 = 9 . y is 9 when x=3.
y=5*46= 14. y is 14 when x= 4.
y=5*56= 19 y is 19 when x= 5
Plot the coordinates: (x,y): (0,6),(1, 1), (2,4) (3,9),(4,14),(5,19).
The easiest way to graph this is to remember the parts of your slopeintercept form. Y and x stand for the coordinates of any points on the line. these will change as you choose a new coordinate pair. the m is your slop. Remember that slope is the change in y ( or rise) over the change in x ( or run). Now, b gives us the value of y where x is zero, this is called the yintercept or where the line will cross the y axis. for you example, y = 5x + 6, this line will intercept or cross the y axis at the point (0, 6). Locate this point on the y axis. now starting from the point (0, 6) we can count the slope. Your slope is the coefficient of your x term. In this instance that is 5, or 5/1. The numerator tells us that the y value for the next coordinate increase by 5, the denominator tells us that the x value for the next coordinate changes by 1, so we can add this values to our starting coordinate of (0, 6). the next point on this line will then be (1, 1). Now do the same process with the new point of (1, 1) . add 5 to the y value and 1 to the x value. The next point is (2, 4). Connect these three points and label to graph it correctly.
Alternately, you could create a table of values, choosing values for x (like 1, 0 and 1) and plugging them into the equation one at a time to solve for the corresponding x coordinate.
The easiest way is to graph it is take the B in this case 6 and graph it by putting a 0 in front of it (0,6) that is your 1st point. Next, take your M, in this case 5 and you go up M points over to the right 1 point or down M points and over to the left 1 point from your B. So your points would be.... (0,6) (1,1) (2,4)
y=mx+b
m= slope if its a whole number put a one under it
rise over run that means you go up however much the numerator is then go over however much the denominator is
b= yintercept that is where it goes over the yaxis
(to graph all possible solutions, a.k.a. to graph the function)
First, note that y=mx+b is lenear, so the graph will be a line. Therefore, you need only two points. Let f(x)=mx+b. Plug in 0 and 1 for x:
f(0)=0+b
f(1)=m+b
Graph the two points (0,b) and (1,[m+b]) and draw a line through them. There is your plot.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. Bertrand Russell :)
m= the slope or how much it goes by. it either goes up or down on the x=axis depending if it's a negative or a positive number.
b= is what to start with where you plot your FIRST point on the yaxis. it either goes on the negative or positive side depending if it's a negative or a positive number.
when you're graphing it, you will start at the first where b is (the staring point) and then go up one over how many m is. you will go left if it's a negative or go right if it's positive and just continue.
when you're solving for y, all you do is use the technic of using the tchart, drawing a line between y and the rest of the equation. for b, you will do the opposite of it, for example: if it's +2, you will do 2 on both sides. if there is no number for x, pretend it's 1, multiply by m, and divide it by 2.
The best way I ever learned to do this was to graph it in sections.
y=mx+b
Start with the slope m, say it is 2/3. Starting from the origin and knowing the slope is rise/run, go up 2 (point is at (0,2)) and them over 3 (point is now at (3,2)). Now with a negative, 4/6, your rise is 4 so you will go down, starting from the orgin, your point is now at (0,4). Now go over to the right 6 now you have the point (6,4). See how the first example (all positive) goes up, left to the right and the second goes down, left to the right. You may also notice that since 4/6 can be reduced to 2/3 it will also go through the point 2/3, and 6/9 since that also can be reduced to 2/3. Something to keep in mind while drawing your graph is that the larger the bottom, or run, is in relationship to the rise the closer the slope will be to the xaxis. Vise versa, if the rise is larger than the run then the slope will be above the 45 degree mark (1/1 slope) and closer to the yaxis.
Next we are going to work with b. b is a shift up or down along the yaxis. So if b=2 then you will shift your entire line up 2 (add 2 to the y of every point) or if it is 7 you will move everything down 7. So let us take the slope 4/6 and shift it up 2. We know three points along this line (2,3), (4,6), and (6,9). Add 2 to each y making them (2,5), (4,8), and (6,11). Draw and connect these points which gives us the line y=4/6(x)+2.
remember to just take everything one at a time and divide the process into smaller managable steps and you'll do fine.
Isn't m the slope and b the y intercept? So can't you just mark (0, 6) on the graph, and then count up 5 and over 1, mark the point (1,1), and draw the line?
the equation y=mx+b is m is the slope and b is the yintercept so if the equation is y=5x+6 6 is the yintercept and 5 is the slope and you can use rise over run and it will be 5 over 1.
plot a point on 6 on the y axis (vertical) then go up 5 over one up five over one now connect all the points with a ruler and draw a line.
y=mx+b
y=5x+6
5=m=slope
6=b=the yintersect
y=5x+6
slope=5/1
yintercept=6
so you start the graph from (0,6)
then the slope=5 rise (go to up or down)
1 run (go right or left)
thats it , its to easy if you was attention in the class girl. :)
y=mx+b
b is the y intercept
m is the slope
x is just x...you can plug in any number and then the out come is apart of your ordered pair (x,y)
Just sub in different values for x and then for y. Start by subbing in a value for x (like 1 or 2 for example) and then make that equal to y, then you'll get a value for y. But you still need a value for x to be able to place it on a graph, so sub in a value for y and solve for x, then you'll have a value for x. Then you have one point which will be (x,y). (sub in the values that you found) Place this point on the graph and keep going until you have enough points to trace a line.
HI,
Ok now , i will try my best to answer this question.
y=mx+b
It is a linear function bcoz the power of variable is 1.
Points:
1) If the linear function we have, so the Graph of this Function is always Straight line.
2)For the Straight line graph, we need at least two points.
3)Y=5x+6, in this equation Y is Dependent variable while X is independent Variable.
4) If we Put the value of X, so we will get the corresponding value of Y.But this Method is not Very Good.
5)We know that at Yintercept the value Of X is always O and at Xintercept the value of Y is always O.
So we find the Two points with the help X and intercepts
First we put Xintercept(X)=O
Y=5(0)+6
Y=6
1st point (0,6)
now we put Yintercept(Y)=O
0=5x+6
5x=6
X=6/5
2nd point (6/5,0)
NOw take these two points and plot the Graph with the help of rules not free hand.
Thanks Alot.
From: Osama Khan.
for y=mx+b,
b = yintercept meaning the point is (0,b)
m = the gradient (how much it slopes)
to find x, put in y=0 > 0=mx+b so x=b/m. this point will then be (b/m, 0)
connect (0,b) and (b/m, 0) and you get the graph :)
so, for y=5x+6, the points are (0,6) and (6/5, 0)
You have to note that y=mx+b is a linear equation, so the graph is a straight line.
In order to build the graph, you have to plug in values for x, and find the values for y.
For tracing the line, it's necessary to have two points. That means having 4 coordinates. You know that a point is defined by its coordinate (x,y).
y=5x6
For x = 0
y = 5*0 6
y = 6
The point has the following coordinates: (0,6)
For x = 1
y = 5*(1) 6=56=11
The point has the following coordinates: (1,11)
Now, in order to graph, trace the system of coordinates, which means two rectangular axes. ox is perpendicular to oy. Choose an unit of measure (for example, if you're working on a math sheet, a unit of measure could be the square from the page)
The negative values, on ox axis, are on the left side and the positive values are on the right side. In the middle of the axis is origin, which has coordinates (0,0).
The negative values, on oy axis, are above origin, and negative values are below origin.
For the point (1,11), on ox axis, number 1 square on the left side and, for oy axis, number 11 squares below origin
make first the table of values of x and y.
i recommend you to use this pattern
x21012 substitute the values of x in the formed equation
y      of y=mx + b.
if you're done solving for y, you can now draw the graph and plot the points together.
it is also advisable to use the other way...
determining the slope and it's yintercept will do.
To put this into simple terms.
y=mx+b
Start your graph by identifying the yintercept which is b.
Next identify your slope, which is m.
So if m=2 and b=3 you would start by placing a point on (0,3).
Then go up 2 and across 1 as m=2 and the slope is rise over run,
meaning if you were to have m=3/4 you would go up 3 and over 4.
Hope this helped in the slightest.
y=5x+6 is in simplest form
m= the slope
b= the yintercept.
the y intercept is where you mark your graph. you would plot a point at (0,6). then the slope basically reads (5/1) (5 over one.) so you would say to yourself "up 5 and over 1" from the yintercept (0,6). You would go up 5 since your slope is positive. If the slope was negative, you would go down 5.
Example Question
y=3x 5
State the slope and yintercept.
the slope would be 3/1 and the y intercept is 5, so you would plot the yintercept at (0,5) and you would say from the point "down 3 and over 1".
Hope that I helped!
this is very simple linear equation. so y=mx+b hmmm...ok u already know that m is ur slope. so if u have an equation like y=2x+1. solve for y.. pretend that u have x=2.
y=2x+1
y=2(2)+1 multiply first and then subtract.
so y is now equal to 5.
your order pairs are (2,5)
plot this order pair.
now look at your m, which is the slope.
now you know that m=2 or 2/1....
m is also known as raise/run. / means over.
after ploting your order pair. you can use you slope,m=2..to move raise two and run one...
m is your slope and b is your yintercept. Make a point at (0,6) and count up 5 and to left 1. You should end with the point (1,1). Draw a line between your two points and you have your line.
y= x6 ,
put x=0 ,we get y=6
i.e one point (0,6) which is on y axis.
put y=0 ,we get x6=0 ,i.e. x=6 ,we have point (6,0) on x axis
join these two point with scale and rule ,extend either side ,it is graph for equation y= x6 ,here slope is m=1 and y intercept=6
you can plot graph of equation y=mx+c in similar way.
You have to note that y=mx+b is a linear equation, so the graph is a straight line. In order to build the graph, you have to plug in values for x, and find the values for y. For tracing the line, it's necessary to have two points. That means having 4
For example: y=5x+6
I don't get how to graph any of it, and I don't get how to add/subtract/multiply/divide any of it.
Note: The coefficient of x is the slope (m) which is 5 and the 6 stands for the yintercept.
let x=0 and let y=0
y=5(0)+(6) 0=5x+(6)
y=06 0=5x6 ; transpose 5x to the left
y=6 side of the equation
(0,6) then change its sign.
5x=6 ; to get the value of x,
divide both sides by 5.
5x/5=6/5
then x=6/5
(6/5,0)
Now you can graph y=5x+6, by ploting these points (0,6) and (6/5,0).....
aj_rockz
Lines are pretty boring but also powerful and very important in your study of mathematics. The basic idea: if you pick any two points on a line and compute the slope, which is "change in y" divided by "change in x", you'll get the same number. ANY two points. No other mathematical shape will have that property.
From this idea comes several forms of the equation of a line. You've asked about the "slopeintercept" form: y = m*x + b.
The "m" stands for "slope" and the "b" is the "yintercept".
Let's talk about the yintercept first. It's called that because it's the yvalue at which the line crosses the yaxis. I.e., the point (0, b) is on the line. Can you see why? Well, let x equal zero. Then y=m*0+b=b, no matter what value "m" has. So yes, the point with x=0 and y=b, called (0,b), is on the line.
Now let's think about slope. Let b=0 and m=2/3 for this conversation. The slope being 2/3 means that if the "change is y" is 2, then the "change in x" must be 3. Let's see that that happens:
Pick any value for x, such as x=5.
Then y=(2/3)*5=10/3.
Let x go up by 3, so x=8.
Now y=(2/3)*8=16/3 so the change in y is (16/3)(10/3)=6/3=2.
With this understanding, you can now graph lines in this form easily:
First graph the point (0,b) since you know that is the yintercept.
Now write the slope as a fraction (perhaps with a denominator of 1). Count "change in y" units up (or down, if that is a negative number) then "change in x" units to the right (or left, if it is a negative number) to get a second point. (You might want to graph three points, just to be sure you're counting correctly.) Then connect the dots!
You should be sure you understand the other form of a line also:
yk=m(xh) which I think is the best, called "pointslope" form
y=5x6
=> 5xy=6
=> 5x/6+y/(6)=1 [dividing both sides by 6]
=> x/(6/5)+y/(6)=1
now mark 6/5 at x axis and 6 at y axis. connect the points with straight line. this is your graph.
first you plug in the slope for m
then you plug in the y intercept for b
then plot your y intercept
finally graph your slope
ex.
y=mx+b
y=3/2x+4
graph this and your graph woul be going through positive 4 on the y intercept and have a slope of 3 over 2
rise = 3

run = 2
y=mx+b is ageneral equation for a straight line.
'm' is th slope(gradient)
m is found by the formula y2y1/x2x1
'b' is the y intercept meaning where the line cuts the y axis.
b is found by substuting the coordinates we have in the equation or by just looking where it cuts the y axis.
having the equation y=5x+6
5 is the gradient
and 6 is where the line y=5x+6 cuts the y axis
The b is your yintersept so you put that in the graph and the m is your slope (rise/run) so you just follow that to find your points on the graph. you should get a straight line.
i think before you do all about y=mx+b you have to find the slope then multiply with the points you did then you will have to equal both sides so you add or subtract or divided or multiply.
for example:
(9,2) (7,1)
21=1
97=2 =.50
y=mx+b
1=1/2(7)
7*.5=3.50
1=3.502.50
y=m2.50
this is how you do and on my math class we are doing slope and today the first time we did the equation and i under stand it but not sure. i hope this helps you.
For example: y=5x+6
I don't get how to graph any of it, and I don't get how to add/subtract/multiply/divide any of it.
Note: The coefficient of x is the slope (m) which is 5 and the 6 stands for the yintercept.
let x=0 and let y=0
y=5(0)+(6) 0=5x+(6)
y=06 0=5x6 ; transpose 5x to the left
y=6 side of the equation
(0,6) then change its sign.
5x=6 ; to get the value of x,
divide both sides by 5.
5x/5=6/5
then x=6/5
(6/5,0)
Now you can graph y=5x+6, by ploting these points (0,6) and (6/5,0).....
B is the y intercept, so you graph it in the y axis. M is the slope, so you do rise over run for that (put into fraction tabs then go up for the numerator and down for the denominatorthat).
the b is your yintersept so you put that in the graph and the m is your slope (rise/run) so you just follow that to find your points on the graph. you should get a straight line.
Put a chart with X and Y...X can be any number...but its easier if its 0,1,2...because it gets u low number and make the graph better...the solve for y...just put in X in the equation and u will find y...which makes ..then you will find (x,y) then graph it.
When you use slope or y=mx+b you have to find m then b. lets say you have y=5x+4, write on the side m=5/1, since 5 is a whole number you write is as a fraction over 1, them b= 4. then you use rise/run . you graph 4 on the y axis the after that you go up +5 and over +1 as may times as you can then if you cant go up any further go down 5 and over 1. (HINT: if its a negtive number go down and to the left.if its positive go up and the to the right.)
y=mx+b
m is the gradient (rise/run) and b is the yintercept.
For example, if the equation is y=2x+3, go to the point (0, 3) and draw a dot. Go 1 across and 2 up to the point (1, 5) and draw another dot. Draw a line through the two dots.
If the equation is y=(2/3)x+4, go to the point (0, 4) and draw a dot. Go 3 across and 2 up to the point (3, 6) and draw another dot. Draw a line through the two dots.
To solve the equation if y=2x+3 and x=4, substitute x for 4:
y=2x+3
y=2*4+3
y=8+3
y=11
Remember that 2x just means "two times x".
Since y=mx+b is a linear equation here is the work which will help:
y = 5x 6 ;
y= 5*06 = 6. y is 6 x=0.
y=5*16 = 1. Y is 1 x=1
y=5*26 = 4. y is 4 x =2.
y=5*36 = 9 . y is 9 x=3.
y=5*46= 14. y is 14 x= 4.
y=5*56= 19 y is 19 x= 5 y= 5x156=69
y=5x6
For x = 0
y = 5*0 6
y = 6
The point has the following coordinates: (0,6)
For x = 1
y = 5*(1) 6=56=11
Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line should solve the equation if you substitute them in the equation for x and y.
The slope (m) of a line can be calculated like so:
m = change in yvalue
change in xvalue
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the yintercept.
The yintercept of this line is the value of y at the point where the line crosses the yaxis.
If I had the equation, y = 2x + 1, my first dot would be positive 1 on the yaxis. After that, I would rise two numbers up on my yaxis and go to the right once, because my yintercept is positive. If your yintercept is negative, you would go to the left. If your slope is negative, you would go below the 0 on your yaxis.
I really hope this helps!
y=mx+b
m< would be your gradient
y< would be your yintercept
in other words m = the slope of your graph
and y = where the line cuts the yaxis.
so your example:
y=5x+6
the "5" is going to be the slope of your graph and the "6" would be where the graph cuts the yaxis.
Since "5" is a positive number, the graph would slope like " / ".
So the graph:
...is really hard to draw on this program...:( sorry.
To graph a linear equation you would substitute values for x to get the y coordinate.
For example:
with an equation like y=2x+4
to graph the equation you would substitute values for x so u would substitute
1 : y=2(1)+4= 6; coordinate: 1,6
and so on
You have to note that y=mx+b is a linear equation, so the graph is a straight line.
The example that you provided is: y = 5x + (6)
m = 5
b = (6)
The variable b indicates the point at which the line crosses the yaxis. Therefore, the coordinates will be: (0,6)
The variable m indicates slope (rise/run). Therefore, you will rise up 5 spaces and will run over 1 space.
Using the variables b and m, you are able to find any point on the line.
1. (0,6)
2. (1,1)
3. (2,4)
4.(3,9)
5.(4,14)
The function y=mx+b represents a linear function, or a straight line. To graph the function y=5x+(6) you must identify M and B. M represent slope which is found in front of the variable x. In this equation your slope (m) is 5. B represents where the line crosses the yaxis, or the yintercept. For this equation your yintercept (b) is 6.
When I graph linear functions I start by plotting my yintercept. Next I follow the slope formula `(rise)/(run)`. You plug in your numbers, in this case it is `(5)/(1)`, and starting with your yintercept move up 5 and over 1. Plot a point each time you do that and you'll have your graph!
When graphing a single y=mx+b, you first take a look at the b, b is the yintercept the yintercept is where the graph meets the vertical yaxis. then you take a look at the m, which is the slope. m= rise over run.
for example,
y=4X +16
16 is the y intercept which can also be written as (0, 16), and 4 is the slope which can also be written as 4/1, so every time you go over one, you go up 4. rise=4, / run =1. by doing this you get all your points on the graph. Now all that's left is drawing the line and you're done!
The answer should be 69, if that is the definite answer you need for the problem.
There are two general ways of solving this problem.
1) You can plug in x values, solve and get a value for y.
For example: y=5x6
if x=0, y=6
So one of your coordinates is (0,6).
2) You can look at the equation and solvw it in y=mx+b
m=slope (rise over run)
b=y intercept
So at (0,6) the graph intercepts the y axis, and if you go up 5 and over 1 pit, tou will get another point, using the slope.
Good Luck.
y=x^2+5x+6
now, factor...
0=(x+2)(x+3)
x=2/3
these is your roots (the points that are on the xaxis)
AOSAxis Of Symmety=middle point
AOS=2.5
plug 2.5 into the original equation
y=(2.5)^2+5(2.5)+6
y=6.25+6.25+6
y=6
your vertex is the lowest point of the graph.
Vertex= (2.5,6)
now graph
:)