Examples

y = 5 x + 4

$y = 5 x + 4$

Step 1

Choose a point that the perpendicular line will pass through.

(0, 0)

$(0, 0)$

Step 2

Use the slope-intercept form to find the slope.

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Step 2.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Using the slope-intercept form, the slope is

5

$5$ .

m = 5

$m = 5$

m = 5

$m = 5$

Step 3

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

m_{perpendicular} = - \frac{1}{5}

$m_{perpendicular} = - \frac{1}{5}$

Step 4

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

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Step 4.1

Use the slope

- \frac{1}{5}

$- \frac{1}{5}$ and a given point

(0, 0)

$(0, 0)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

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

y - y_{1} = m (x - x_{1})

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

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

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

y - (0) = - \frac{1}{5} \cdot (x - (0))

$y - (0) = - \frac{1}{5} \cdot (x - (0))$

Step 4.2

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

y + 0 = - \frac{1}{5} \cdot (x + 0)

$y + 0 = - \frac{1}{5} \cdot (x + 0)$

y + 0 = - \frac{1}{5} \cdot (x + 0)

$y + 0 = - \frac{1}{5} \cdot (x + 0)$

Step 5

Write in

y = m x + b

$y = m x + b$ form.

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Step 5.1

Solve for

y

$y$ .

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Step 5.1.1

Add

y

$y$ and

0

$0$ .

y = - \frac{1}{5} \cdot (x + 0)

$y = - \frac{1}{5} \cdot (x + 0)$

Step 5.1.2

Simplify

- \frac{1}{5} \cdot (x + 0)

$- \frac{1}{5} \cdot (x + 0)$ .

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Step 5.1.2.1

Add

x

$x$ and

0

$0$ .

y = - \frac{1}{5} \cdot x

$y = - \frac{1}{5} \cdot x$

Step 5.1.2.2

Combine

x

$x$ and

\frac{1}{5}

$\frac{1}{5}$ .

y = - \frac{x}{5}

$y = - \frac{x}{5}$

y = - \frac{x}{5}

$y = - \frac{x}{5}$

y = - \frac{x}{5}

$y = - \frac{x}{5}$

Step 5.2

Reorder terms.

y = - (\frac{1}{5} x)

$y = - (\frac{1}{5} x)$

Step 5.3

Remove parentheses.

y = - \frac{1}{5} x

$y = - \frac{1}{5} x$

y = - \frac{1}{5} x

$y = - \frac{1}{5} x$

Step 6

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