Examples

$y = 3 x - 21$ ,

$(- 7, 0)$

Step 1

Use the slope-intercept form to find the slope.

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Step 1.1

The slope-intercept form is

$y = m x + b$ , where

$m$ is the slope and

$b$ is the y-intercept.

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is

$3$ .

$m = 3$

Step 2

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

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

Step 3

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

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Step 3.1

Use the slope

$- \frac{1}{3}$ and a given point

$(- 7, 0)$ to substitute for

$x_{1}$ and

$y_{1}$ in the point-slope form

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 3.2

Simplify the equation and keep it in point-slope form.

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

Step 4

Write in

$y = m x + b$ form.

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Step 4.1

Solve for

$y$ .

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Step 4.1.1

Add

$y$ and

$0$ .

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

Step 4.1.2

Simplify

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

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Step 4.1.2.1

Apply the distributive property.

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

Step 4.1.2.2

Combine

$x$ and

$\frac{1}{3}$ .

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

Step 4.1.2.3

Multiply

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

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Step 4.1.2.3.1

Multiply

$7$ by

$- 1$ .

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

Step 4.1.2.3.2

Combine

$- 7$ and

$\frac{1}{3}$ .

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

Step 4.1.2.4

Move the negative in front of the fraction.

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

Step 4.2

Reorder terms.

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

Step 4.3

Remove parentheses.

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

Step 5

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