Precalculus Examples

$y = \frac{1}{6} x + 4$

Step 1

Rewrite in slope-intercept form.

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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

Simplify the right side.

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Step 1.2.1

Combine $\frac{1}{6}$ and $x$ .

$y = \frac{x}{6} + 4$

Step 1.3

Reorder terms.

$y = \frac{1}{6} x + 4$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{6}$ .

$m = \frac{1}{6}$

Step 3

The equation of a perpendicular line to $y = \frac{1}{6} x + 4$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{1}{6}}$

Step 4

Simplify the result.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 6)$

Step 4.2

Multiply $- (1 \cdot 6)$ .

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Step 4.2.1

Multiply $6$ by $1$ .

$m_{perpendicular} = - 1 \cdot 6$

Step 4.2.2

Multiply $- 1$ by $6$ .

$m_{perpendicular} = - 6$

Step 5