Precalculus Examples

Find Any Equation Perpendicular to the Line
Choose a point that the perpendicular line will pass through.
Solve .
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Rewrite the equation as .
Add to both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Use the slope-intercept form to find the slope.
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The slope-intercept form is , where is the slope and is the y-intercept.
Using the slope-intercept form, the slope is .
The equation of a perpendicular line to must have a slope that is the negative reciprocal of the original slope.
Simplify to find the slope of the perpendicular line.
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Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Find the equation of the perpendicular line using the point-slope formula.
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Using the point-slope form , plug in , , and .
Solve for .
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Subtract from .
Simplify .
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Subtract from .
Combine and .
Move to the left of .
Reorder terms.
Remove parentheses.
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