Find the Slope of a Perpendicular Line 12x+4y=16

$12 x + 4 y = 16$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Subtract $12 x$ from both sides of the equation.

$4 y = 16 - 12 x$

Divide each term in $4 y = 16 - 12 x$ by $4$ and simplify.

Divide each term in $4 y = 16 - 12 x$ by $4$ .

$\frac{4 y}{4} = \frac{16}{4} + \frac{- 12 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{16}{4} + \frac{- 12 x}{4}$

Divide $y$ by $1$ .

$y = \frac{16}{4} + \frac{- 12 x}{4}$

Simplify the right side.

Simplify each term.

Divide $16$ by $4$ .

$y = 4 + \frac{- 12 x}{4}$

Cancel the common factor of $- 12$ and $4$ .

Factor $4$ out of $- 12 x$ .

$y = 4 + \frac{4 (- 3 x)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = 4 + \frac{4 (- 3 x)}{4 (1)}$

Cancel the common factor.

$y = 4 + \frac{4 (- 3 x)}{4 \cdot 1}$

Rewrite the expression.

$y = 4 + \frac{- 3 x}{1}$

Divide $- 3 x$ by $1$ .

$y = 4 - 3 x$

Reorder $4$ and $- 3 x$ .

$y = - 3 x + 4$

Step 2

Using the slope-intercept form, the slope is $- 3$ .

$m = - 3$

Step 3

The equation of a perpendicular line to $y = - 3 x + 4$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Move the negative in front of the fraction.

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

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

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{1}{3})$

Multiply $\frac{1}{3}$ by $1$ .

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

Step 5

Find the Slope of a Perpendicular Line 12x+4y=16

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