# Precalculus Examples

Find the Equation Using Two Points
,
Step 1
Use to calculate the equation of the line, where represents the slope and represents the y-intercept.
To calculate the equation of the line, use the format.
Step 2
Slope is equal to the change in over the change in , or rise over run.
Step 3
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 4
Substitute in the values of and into the equation to find the slope.
Step 5
Finding the slope .
Step 5.1
Simplify the numerator.
Step 5.1.1
Multiply by .
Step 5.1.2
Subtract from .
Step 5.2
Simplify the denominator.
Step 5.2.1
Multiply by .
Step 5.2.2
Subtract from .
Step 5.3
Divide by .
Step 6
Find the value of using the formula for the equation of a line.
Step 6.1
Use the formula for the equation of a line to find .
Step 6.2
Substitute the value of into the equation.
Step 6.3
Substitute the value of into the equation.
Step 6.4
Substitute the value of into the equation.
Step 6.5
Find the value of .
Step 6.5.1
Rewrite the equation as .
Step 6.5.2
Multiply by .
Step 6.5.3
Move all terms not containing to the right side of the equation.
Step 6.5.3.1
Subtract from both sides of the equation.
Step 6.5.3.2
Subtract from .
Step 7
Now that the values of (slope) and (y-intercept) are known, substitute them into to find the equation of the line.
Step 8