Precalculus Examples

Find the Perpendicular Line
,
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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Move the negative in front of the fraction.
Multiply .
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Multiply by .
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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Multiply by .
Simplify .
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Multiply by .
Apply the distributive property.
Combine and .
Combine and .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Simplify the right side of the equation.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
Reorder terms.
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