(6,-1) , (-21,17)

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=17-(-1)-21-(6)

Simplify.

Simplify the numerator.

Multiply -1 by -1.

m=17+1-21-(6)

Add 17 and 1.

m=18-21-(6)

m=18-21-(6)

Simplify the denominator.

Multiply -1 by 6.

m=18-21-6

Subtract 6 from -21.

m=18-27

m=18-27

Reduce the expression by cancelling the common factors.

Cancel the common factor of 18 and -27.

Factor 9 out of 18.

m=9(2)-27

Cancel the common factors.

Factor 9 out of -27.

m=9⋅29⋅-3

Cancel the common factor.

m=9⋅29⋅-3

Rewrite the expression.

m=2-3

m=2-3

m=2-3

Move the negative in front of the fraction.

m=-23

m=-23

m=-23

m=-23

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

y=(-23)⋅x+b

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

y=(-23)⋅(6)+b

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

-1=(-23)⋅(6)+b

Rewrite the equation as (-23)⋅(6)+b=-1.

(-23)⋅(6)+b=-1

Simplify each term.

Cancel the common factor of 3.

Move the leading negative in -23 into the numerator.

-23⋅6+b=-1

Factor 3 out of 6.

-23⋅(3(2))+b=-1

Cancel the common factor.

-23⋅(3⋅2)+b=-1

Rewrite the expression.

-2⋅2+b=-1

-2⋅2+b=-1

Multiply -2 by 2.

-4+b=-1

-4+b=-1

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

Add 4 to both sides of the equation.

b=-1+4

Add -1 and 4.

b=3

b=3

b=3

The values of the slope and y-intercept are m=-23 and b=3.

m=-23

b=3

Find the Slope and Y-Intercept (6,-1) , (-21,17)