# Precalculus Examples

Find the Equation Using Point-Slope Formula
,
Step 1
Find the slope of the line between and using , which is the change of over the change of .
Step 1.1
Slope is equal to the change in over the change in , or rise over run.
Step 1.2
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).
Step 1.3
Substitute in the values of and into the equation to find the slope.
Step 1.4
Simplify.
Step 1.4.1
Simplify the numerator.
Step 1.4.1.1
Multiply by .
Step 1.4.1.2
Step 1.4.2
Simplify the denominator.
Step 1.4.2.1
Multiply by .
Step 1.4.2.2
Subtract from .
Step 1.4.3
Divide by .
Step 2
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 3
Simplify the equation and keep it in point-slope form.
Step 4
Solve for .
Step 4.1
Simplify .
Step 4.1.1
Rewrite.
Step 4.1.2
Step 4.1.3
Apply the distributive property.
Step 4.1.4
Multiply by .
Step 4.2
Move all terms not containing to the right side of the equation.
Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Subtract from .
Step 5
List the equation in different forms.
Slope-intercept form:
Point-slope form:
Step 6