(-4,9) , (2,-3)

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=-3-(9)2-(-4)

Simplify.

Simplify the numerator.

Multiply -1 by 9.

m=-3-92-(-4)

Subtract 9 from -3.

m=-122-(-4)

m=-122-(-4)

Simplify the denominator.

Multiply -1 by -4.

m=-122+4

Add 2 and 4.

m=-126

m=-126

Divide -12 by 6.

m=-2

m=-2

m=-2

Use the slope -2 and a given point (-4,9) to substitute for x1 and y1 in the point-slope form y-y1=m(x-x1), which is derived from the slope equation m=y2-y1x2-x1.

y-(9)=(-2)(x-(-4))

Simplify the equation and keep it in point-slope form.

y-9=-2⋅(x+4)

Simplify -2⋅(x+4).

Apply the distributive property.

y-9=-2x-2⋅4

Multiply -2 by 4.

y-9=-2x-8

y-9=-2x-8

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

Add 9 to both sides of the equation.

y=-2x-8+9

Add -8 and 9.

y=-2x+1

y=-2x+1

y=-2x+1

List the equation in different forms.

Slope-intercept form:

y=-2x+1

Point-slope form:

y-9=-2⋅(x+4)

Find the Equation Using Point-Slope Form (-4,9) , (2,-3)