# Precalculus Examples

Find the Perpendicular Line
,
Step 1
Use the slope-intercept form to find the slope.
The slope-intercept form is , where is the slope and is the y-intercept.
Using the slope-intercept form, the slope is .
Step 2
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Step 3
Simplify to find the slope of the perpendicular line.
Move the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
Step 4
Find the equation of the perpendicular line using the point-slope formula.
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.
Step 5
Write in form.
Solve for .
Simplify .
Rewrite.
Apply the distributive property.
Combine and .
Combine and .
Move all terms not containing to the right side of the equation.
Subtract from both sides 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 .
Subtract from .
Move the negative in front of the fraction.
Reorder terms.
Step 6