# Find the Equation Using Point-Slope Formula (-5,9) , (3,0) (-5,9) , (3,0)
Find the slope of the line between (-5,9) and (3,0) using m=y2-y1x2-x1, which is the change of y over the change of x.
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)
Solve for y.
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)

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