(-5,9) , (3,0)

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=0-(9)3-(-5)

Simplify.

Simplify the numerator.

Multiply -1 by 9.

m=0-93-(-5)

Subtract 9 from 0.

m=-93-(-5)

m=-93-(-5)

Simplify the denominator.

Multiply -1 by -5.

m=-93+5

Add 3 and 5.

m=-98

m=-98

Move the negative in front of the fraction.

m=-98

m=-98

m=-98

Use the slope -98 and a given point (-5,9) 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)=(-98)(x-(-5))

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

y-9=-98⋅(x+5)

Simplify -98⋅(x+5).

Apply the distributive property.

y-9=-98x-98⋅5

Combine x and 98.

y-9=-x⋅98-98⋅5

Multiply -98⋅5.

Multiply 5 by -1.

y-9=-x⋅98-5(98)

Combine -5 and 98.

y-9=-x⋅98+-5⋅98

Multiply -5 by 9.

y-9=-x⋅98+-458

y-9=-x⋅98+-458

Simplify each term.

Move 9 to the left of x.

y-9=-9⋅x8+-458

Move the negative in front of the fraction.

y-9=-9×8-458

y-9=-9×8-458

y-9=-9×8-458

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

Add 9 to both sides of the equation.

y=-9×8-458+9

To write 9 as a fraction with a common denominator, multiply by 88.

y=-9×8-458+9⋅88

Combine 9 and 88.

y=-9×8-458+9⋅88

Combine the numerators over the common denominator.

y=-9×8+-45+9⋅88

Simplify the numerator.

Multiply 9 by 8.

y=-9×8+-45+728

Add -45 and 72.

y=-9×8+278

y=-9×8+278

y=-9×8+278

y=-9×8+278

Reorder terms.

y=-(98x)+278

Remove parentheses.

y=-98x+278

List the equation in different forms.

Slope-intercept form:

y=-98x+278

Point-slope form:

y-9=-98⋅(x+5)

Find the Equation Using Point-Slope Formula (-5,9) , (3,0)