Find the Slope of a Parallel Line 2x+6y=1

$2 x + 6 y = 1$

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 $2 x$ from both sides of the equation.

$6 y = 1 - 2 x$

Divide each term in $6 y = 1 - 2 x$ by $6$ and simplify.

Divide each term in $6 y = 1 - 2 x$ by $6$ .

$\frac{6 y}{6} = \frac{1}{6} + \frac{- 2 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{1}{6} + \frac{- 2 x}{6}$

Divide $y$ by $1$ .

$y = \frac{1}{6} + \frac{- 2 x}{6}$

Simplify the right side.

Simplify each term.

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

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

$y = \frac{1}{6} + \frac{2 (- x)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$y = \frac{1}{6} + \frac{2 (- x)}{2 (3)}$

Cancel the common factor.

$y = \frac{1}{6} + \frac{2 (- x)}{2 \cdot 3}$

Rewrite the expression.

$y = \frac{1}{6} + \frac{- x}{3}$

Move the negative in front of the fraction.

$y = \frac{1}{6} - \frac{x}{3}$

Write in $y = m x + b$ form.

Reorder $\frac{1}{6}$ and $- \frac{x}{3}$ .

$y = - \frac{x}{3} + \frac{1}{6}$

Reorder terms.

$y = - (\frac{1}{3} x) + \frac{1}{6}$

Remove parentheses.

$y = - \frac{1}{3} x + \frac{1}{6}$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{3}$ .

$m = - \frac{1}{3}$

Step 3

All lines that are parallel to $y = - \frac{1}{3} x + \frac{1}{6}$ have the same slope of $- \frac{1}{3}$ .

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

Step 4