Precalculus Examples

Find Any Equation Perpendicular to the Line
Step 1
Choose a point that the perpendicular line will pass through.
Step 2
Solve .
Tap for more steps...
Step 2.1
Subtract from both sides of the equation.
Step 2.2
Divide each term in by and simplify.
Tap for more steps...
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Tap for more steps...
Step 2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Tap for more steps...
Step 2.2.3.1
Move the negative in front of the fraction.
Step 3
Find the slope when .
Tap for more steps...
Step 3.1
Rewrite in slope-intercept form.
Tap for more steps...
Step 3.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 3.1.2
Write in form.
Tap for more steps...
Step 3.1.2.1
Reorder terms.
Step 3.1.2.2
Remove parentheses.
Step 3.2
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.
Tap for more steps...
Step 5.1
Cancel the common factor of and .
Tap for more steps...
Step 5.1.1
Rewrite as .
Step 5.1.2
Move the negative in front of the fraction.
Step 5.2
Multiply the numerator by the reciprocal of the denominator.
Step 5.3
Multiply by .
Step 5.4
Multiply .
Tap for more steps...
Step 5.4.1
Multiply by .
Step 5.4.2
Multiply by .
Step 6
Find the equation of the perpendicular line using the point-slope formula.
Tap for more steps...
Step 6.1
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 6.2
Simplify the equation and keep it in point-slope form.
Step 7
Write in form.
Tap for more steps...
Step 7.1
Solve for .
Tap for more steps...
Step 7.1.1
Add and .
Step 7.1.2
Simplify .
Tap for more steps...
Step 7.1.2.1
Add and .
Step 7.1.2.2
Combine and .
Step 7.2
Reorder terms.
Step 8
Enter YOUR Problem
Mathway requires javascript and a modern browser.