(4,-3) , (-2,-5)

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=-5-(-3)-2-(4)

Simplify.

Simplify the numerator.

Multiply -1 by -3.

m=-5+3-2-(4)

Add -5 and 3.

m=-2-2-(4)

m=-2-2-(4)

Simplify the denominator.

Multiply -1 by 4.

m=-2-2-4

Subtract 4 from -2.

m=-2-6

m=-2-6

Cancel the common factor of -2 and -6.

Factor -2 out of -2.

m=-2⋅1-6

Cancel the common factors.

Factor -2 out of -6.

m=-2⋅1-2⋅3

Cancel the common factor.

m=-2⋅1-2⋅3

Rewrite the expression.

m=13

m=13

m=13

m=13

m=13

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

y=(13)x+b

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

y=(13)⋅(4)+b

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

-3=(13)⋅(4)+b

Rewrite the equation as (13)⋅(4)+b=-3.

(13)⋅(4)+b=-3

Combine 13 and 4.

43+b=-3

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

Subtract 43 from both sides of the equation.

b=-3-43

To write -3 as a fraction with a common denominator, multiply by 33.

b=-3⋅33-43

Combine -3 and 33.

b=-3⋅33-43

Combine the numerators over the common denominator.

b=-3⋅3-43

Simplify the numerator.

Multiply -3 by 3.

b=-9-43

Subtract 4 from -9.

b=-133

b=-133

Move the negative in front of the fraction.

b=-133

b=-133

b=-133

The values of the slope and y-intercept are m=13 and b=-133.

m=13

b=-133

Find the Slope and Y-Intercept (4,-3) , (-2,-5)