Precalculus Examples

$y = x - 2$ , $(2, 6)$

Use the slope-intercept form to find the slope.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Using the slope-intercept form, the slope is $1$ .

$m = 1$

The equation of a perpendicular line to $y = x - 2$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{1}$

Simplify $- \frac{1}{1}$ to find the slope of the perpendicular line.

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Divide $1$ by $1$ .

$m_{perpendicular} = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$m_{perpendicular} = - 1$

Find the equation of the perpendicular line using the point-slope formula.

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Using the point-slope form $y - y_{1} = m (x - x_{1})$ , plug in $m = - 1$ , $x_{1} = 2$ , and $y_{1} = 6$ .

$y - (6) = (- 1) (x - (2))$

Solve for $y$ .

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Multiply $- 1$ by $6$ .

$y - 6 = (- 1) (x - (2))$

Simplify $(- 1) (x - (2))$ .

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Multiply $- 1$ by $2$ .

$y - 6 = - 1 (x - 2)$

Apply the distributive property.

$y - 6 = - 1 x - 1 \cdot - 2$

Simplify the expression.

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Rewrite $- 1 x$ as $- x$ .

$y - 6 = - x - 1 \cdot - 2$

Multiply $- 1$ by $- 2$ .

$y - 6 = - x + 2$

Move all terms not containing $y$ to the right side of the equation.

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Add $6$ to both sides of the equation.

$y = - x + 2 + 6$

Add $2$ and $6$ .

$y = - x + 8$

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