Find the slope and y-intercept of the line given by y = 5x + 4 . Find the coordinates of a point, other than ( 0 , b ) on the line.
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First, let's write the general form of the equation of the line:
y=mx+b, where m represents the slope and b represents the y intercept.
Analyizing the given equation of the line, y = 5x + 4, we'll conclude: m=5 and b=4.
To find out another point which belongs to the given line, we'll just have to input another value for x, other than x=0.
We'll set x=1.
y = 5*1 + 4
y = 9
So, another point on the line is P(1,9).
Any line of the form y = mx+c is a straight line which has a slope m and it makes an intercept of C on y axis.
The given line , y= 5x+c has a slope 5 and it intercepts y axis at 4 units anbove the origin.
Slope 5 means the line is inclined x degrees and tanx = 5.
Also we can get the y intercept by putting x =0 in y = 5x+4: y = 5*0+4 =4. Or (0,4) is a point on y =5x+4.
To get a point other than (0,4) 0n y = 5x+4. Let the x coordinate be 1, the y = 5*1+4 = 9. So (1,9) is a point other than (0,b)
Let y = 0, then fron y=5x+4 becomes, 0= 5x+4 , or x = -4/5. So, (4/5,0) is another point on the line. And 4/5 is the X intercept of the line on X axis.
y = 5x + 4 is written in slope-intercept form. Recall that slope-intercept form is:
y = mx+b where m is the slope and b is the y-intercept.
Knowing this, its easy to identify the slope. To find the coordinates of a point other than (0, b), pick any x value you like and plug it in to determine the corresponding y value.
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