# Algebra Examples

Find the Equation Using Point-Slope Formula
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Find the slope of the line between and using , which is the change of over the change of .
Slope is equal to the change in over the change in , or rise over run.
The change in is equal to the difference in x-coordinates (also called run), and the change in is equal to the difference in y-coordinates (also called rise).
Substitute in the values of and into the equation to find the slope.
Simplify.
Simplify the numerator.
Multiply by .
Subtract from .
Simplify the denominator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Use the slope and one of the given points such as to substitute for and in the point-slope form , which is derived from the slope equation .
Solve for to get the equation.
Multiply by .
Simplify .
Multiply by .
Apply the distributive property.
Combine and .
Multiply .
Multiply by .
Combine and .
Multiply by .
Move to the left of .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Simplify the right side of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .