(2,23) , (6,18)

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=18-(23)6-(2)

Simplify.

Simplify the numerator.

Multiply -1 by 23.

m=18-236-(2)

Subtract 23 from 18.

m=-56-(2)

m=-56-(2)

Simplify the denominator.

Multiply -1 by 2.

m=-56-2

Subtract 2 from 6.

m=-54

m=-54

Move the negative in front of the fraction.

m=-54

m=-54

m=-54

Substitute the value of m into the slope-intercept form of the equation, y=mx+b.

y=(-54)⋅x+b

Substitute the value of x into the slope-intercept form of the equation, y=mx+b.

y=(-54)⋅(2)+b

Substitute the value of y into the slope-intercept form of the equation, y=mx+b.

23=(-54)⋅(2)+b

Rewrite the equation as (-54)⋅(2)+b=23.

(-54)⋅(2)+b=23

Simplify each term.

Cancel the common factor of 2.

Move the leading negative in -54 into the numerator.

-54⋅2+b=23

Factor 2 out of 4.

-52(2)⋅2+b=23

Cancel the common factor.

-52⋅2⋅2+b=23

Rewrite the expression.

-52+b=23

-52+b=23

Move the negative in front of the fraction.

-52+b=23

-52+b=23

Move all terms not containing b to the right side of the equation.

Add 52 to both sides of the equation.

b=23+52

To write 23 as a fraction with a common denominator, multiply by 22.

b=23⋅22+52

Combine 23 and 22.

b=23⋅22+52

Combine the numerators over the common denominator.

b=23⋅2+52

Simplify the numerator.

Multiply 23 by 2.

b=46+52

Add 46 and 5.

b=512

b=512

b=512

b=512

The values of the slope and y-intercept are m=-54 and b=512.

m=-54

b=512

Find the Slope and Y-Intercept (2,23) , (6,18)