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

$2 y - 6 x = - 2$

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.

$y = m x + b$

Add $6 x$ to both sides of the equation.

$2 y = - 2 + 6 x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

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

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

Factor $2$ out of $6 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 x$ by $1$ .

$y = - 1 + 3 x$

Reorder $- 1$ and $3 x$ .

$y = 3 x - 1$

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

$m = 3$

All lines that are parallel to $y = 3 x - 1$ have the same slope of $3$ .

$m_{parallel} = 3$