Find the Slope of a Parallel Line 6x-3y=-2

$6 x - 3 y = - 2$

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.

$- 3 y = - 2 - 6 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Cancel the common factor of $- 6$ and $- 3$ .

Factor $- 3$ out of $- 6 x$ .

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

Cancel the common factors.

Factor $- 3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x$ by $1$ .

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

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

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

Step 2

Using the slope-intercept form, the slope is $2$ .

$m = 2$

Step 3

All lines that are parallel to $y = 2 x + \frac{2}{3}$ have the same slope of $2$ .

$m_{parallel} = 2$

Step 4