# Find the Equation Using Point-Slope Formula (2,5) , (6,7)

,
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 .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Simplify the equation and keep it in point-slope form.
Solve for .
Simplify .
Apply the distributive property.
Combine and .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.