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.

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

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

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

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

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Multiply $- 7$ by $- 1$ .

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

Combine $7$ and $\frac{1}{3}$ .

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

Reorder terms.

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

Remove parentheses.

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

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