# Find the Equation Using Point-Slope Form (-4,9) , (2,-3) (-4,9) , (2,-3)
Find the slope of the line between (-4,9) and (2,-3) 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=-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)
Solve for y.
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)

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