Precalculus Examples

$y = 3 x - 21$ , $(- 7, 0)$

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 $3$ .

$m = 3$

The equation of a perpendicular line to $y = 3 x - 21$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{3}$

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 $m = - \frac{1}{3}$ , $x_{1} = - 7$ , and $y_{1} = 0$ .

$y - (0) = (- \frac{1}{3}) (x - (- 7))$

Solve for $y$ .

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Subtract $0$ from $y$ .

$y = (- \frac{1}{3}) (x - (- 7))$

Simplify $(- \frac{1}{3}) (x - (- 7))$ .

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Multiply $- 1$ by $- 7$ .

$y = - \frac{1}{3} \cdot (x + 7)$

Apply the distributive property.

$y = - \frac{1}{3} x - \frac{1}{3} \cdot 7$

Simplify $- \frac{1}{3} x$ .

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Write $x$ as a fraction with denominator $1$ .

$y = - (\frac{x}{1} \cdot \frac{1}{3}) - \frac{1}{3} \cdot 7$

Multiply $\frac{x}{1}$ and $\frac{1}{3}$ .

$y = - \frac{x}{3} - \frac{1}{3} \cdot 7$

Simplify $- \frac{1}{3} \cdot 7$ .

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Multiply $7$ by $- 1$ .

$y = - \frac{x}{3} - 7 (\frac{1}{3})$

Write $- 7$ as a fraction with denominator $1$ .

$y = - \frac{x}{3} + \frac{- 7}{1} \cdot \frac{1}{3}$

Multiply $\frac{- 7}{1}$ and $\frac{1}{3}$ .

$y = - \frac{x}{3} + \frac{- 7}{3}$

Move the negative in front of the fraction.

$y = - \frac{x}{3} - \frac{7}{3}$

Reorder terms.

$y = - (\frac{1}{3} x) - \frac{7}{3}$

Remove parentheses.

$y = - \frac{1}{3} x - \frac{7}{3}$

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