# Algebra Examples

Find Any Equation Perpendicular to the Line
Step 1
Choose a point that the perpendicular line will pass through.
Step 2
Solve .
Subtract from both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Move the negative in front of the fraction.
Step 3
Find the slope when .
Rewrite in slope-intercept form.
The slope-intercept form is , where is the slope and is the y-intercept.
Write in form.
Reorder terms.
Remove parentheses.
Using the slope-intercept form, the slope is .
Step 4
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Step 5
Simplify to find the slope of the perpendicular line.
Cancel the common factor of and .
Rewrite as .
Move the negative in front of the fraction.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Multiply .
Multiply by .
Multiply by .
Step 6
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 7
Write in form.
Solve for .