(9,4) , (13,6)

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

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)