Find the Slope of a Perpendicular Line 6x+2y=3

$6 x + 2 y = 3$

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 $6 x$ from both sides of the equation.

$2 y = 3 - 6 x$

Divide each term in $2 y = 3 - 6 x$ by $2$ and simplify.

Divide each term in $2 y = 3 - 6 x$ by $2$ .

$\frac{2 y}{2} = \frac{3}{2} + \frac{- 6 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{3}{2} + \frac{- 6 x}{2}$

Divide $y$ by $1$ .

$y = \frac{3}{2} + \frac{- 6 x}{2}$

Simplify the right side.

Cancel the common factor of $- 6$ and $2$ .

Factor $2$ out of $- 6 x$ .

$y = \frac{3}{2} + \frac{2 (- 3 x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{3}{2} + \frac{2 (- 3 x)}{2 (1)}$

Cancel the common factor.

$y = \frac{3}{2} + \frac{2 (- 3 x)}{2 \cdot 1}$

Rewrite the expression.

$y = \frac{3}{2} + \frac{- 3 x}{1}$

Divide $- 3 x$ by $1$ .

$y = \frac{3}{2} - 3 x$

Reorder $\frac{3}{2}$ and $- 3 x$ .

$y = - 3 x + \frac{3}{2}$

Step 2

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

$m = - 3$

Step 3

The equation of a perpendicular line to $y = - 3 x + \frac{3}{2}$ 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 6x+2y=3

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