# Find the Slope and Y-Intercept (9,4) , (13,6) (9,4) , (13,6)
Find the value of the slope.
Slope is equal to the change in y over the change in x, or rise over run.
m=change in ychange in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=y2-y1x2-x1
Substitute in the values of x and y into the equation to find the slope.
m=6-(4)13-(9)
Simplify.
Simplify the numerator.
Multiply -1 by 4.
m=6-413-(9)
Subtract 4 from 6.
m=213-(9)
m=213-(9)
Simplify the denominator.
Multiply -1 by 9.
m=213-9
Subtract 9 from 13.
m=24
m=24
Cancel the common factor of 2 and 4.
Factor 2 out of 2.
m=2(1)4
Cancel the common factors.
Factor 2 out of 4.
m=2⋅12⋅2
Cancel the common factor.
m=2⋅12⋅2
Rewrite the expression.
m=12
m=12
m=12
m=12
m=12
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(12)x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(12)⋅(9)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
4=(12)⋅(9)+b
Rewrite the equation as (12)⋅(9)+b=4.
(12)⋅(9)+b=4
Combine 12 and 9.
92+b=4
Move all terms not containing b to the right side of the equation.
Subtract 92 from both sides of the equation.
b=4-92
To write 4 as a fraction with a common denominator, multiply by 22.
b=4⋅22-92
Combine 4 and 22.
b=4⋅22-92
Combine the numerators over the common denominator.
b=4⋅2-92
Simplify the numerator.
Multiply 4 by 2.
b=8-92
Subtract 9 from 8.
b=-12
b=-12
Move the negative in front of the fraction.
b=-12
b=-12
b=-12
The values of the slope and y-intercept are m=12 and b=-12.
m=12
b=-12
Find the Slope and Y-Intercept (9,4) , (13,6)     