``slope 3, passes through (-2, 4)`` Write an equation in slope-intercept form that satisfies each set of conditions.
If we know that the slope of our line is 3 and the point that it is passing through is (-2,4), then we can use slope-intercept form to solve it. The formula y=mx+b. In this formula the m represents the slope, the x and y represent the coordinates of the point, and the b represents the y-intercept (where it crosses the y axis of the graph). Let's begin by plugging in what we know:
4=3(-2)+b Our first step is to solve for b so that we can find our intercept.
Once we know what our y-intercept (b) is, we can the go back to our original equation and rewrite it so that it is in slope-intercept form. In slope-intercept form the values of x and y are left out so that other points along the line can be determined. Therefore our solution will be y=3x+10
Equation of the line having slope 'm' & passing through a point (a,b) is :-
y - b = m(x-a)
The standard for of representing a line in slope-intercept form is :-
y = mx + b ; where m = slope of the line & 'b' = y-intercept
Now, the line passes through the point (-2,4) & has slope 3
Thus, equation of the line is :-
y - (4) = 3*(x-(-2))
or, y - 4 = 3x + 6
or, y = 3x + 10 = slope-intercept representation of the line
The slope intercept-form of an equation of a line is y=mx+b
Given that the slope is 3 and a point on the line is P(-2, 4), then
m=3 and from the point (-2, 4), x=-2 and y=4.
Substitute the m, x, and y into the slope intercept form
4=3(-2)+b Now solve for b.
Now you know b=10 and you already know the slope m=3. Substitute these values into y=mx+b. When you do you will get y=3x+10. This is your answer in slope intercept form.
The slope (m) as given in the question is 3 which means m=3.
You are given points (-2,4) through which the line passes.
As you may recall, the slope intercept form is y=m*x+b, where:
m=slope = 3
x=x point = -2
y=y point = 4
b=constant = ?(you have to figure it out!)
- So you just plug in the values for the variables and solve for b
4 = 3*(-2)+b
4 = -6+b
Once you have solved for b, you simply plug it in the equation y=m*x+b
So, y = 3x + 10 is the equation that has a slope of 3 and passes through (-2,4)
Note: For the final equation, you only need to plug in the value of m and b. ( as seen above) For y and x you just write y and x , not the numerical value.
Hope this helps!
Given `m= 3` and the line passes through the point `(x_1,y_1)=(-2,4)`
the slope-intercept form is `y= mx+b`
we can find the equation of the line as
=>` (y - 4)= 3(x-(-2))`
=> `(y-4)= 3(x+2)`
=> `y-4= 3x+6`
=> `y = 3x+10`
is the slope-intercept form