Precalculus Examples

$y = x - 9$ , $(0, 0)$

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 $y = x - 9$ 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 $m = - 1$ , $x_{1} = 0$ , and $y_{1} = 0$ .

$y - (0) = (- 1) (x - (0))$

Solve for $y$ .

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Subtract $0$ from $y$ .

$y = (- 1) (x - (0))$

Simplify $(- 1) (x - (0))$ .

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Subtract $0$ from $x$ .

$y = - 1 x$

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

$y = - x$

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