Find the Slope of a Parallel Line 9x+6y=-6

$9 x + 6 y = - 6$

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 $9 x$ from both sides of the equation.

$6 y = - 6 - 9 x$

Divide each term in $6 y = - 6 - 9 x$ by $6$ and simplify.

Divide each term in $6 y = - 6 - 9 x$ by $6$ .

$\frac{6 y}{6} = \frac{- 6}{6} + \frac{- 9 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 6}{6} + \frac{- 9 x}{6}$

Divide $y$ by $1$ .

$y = \frac{- 6}{6} + \frac{- 9 x}{6}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $6$ .

$y = - 1 + \frac{- 9 x}{6}$

Cancel the common factor of $- 9$ and $6$ .

Factor $3$ out of $- 9 x$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

Reorder $- 1$ and $- \frac{3 x}{2}$ .

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

Reorder terms.

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

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{2}$ .

$m = - \frac{3}{2}$

Step 3

All lines that are parallel to $y = - \frac{3}{2} x - 1$ have the same slope of $- \frac{3}{2}$ .

$m_{parallel} = - \frac{3}{2}$

Step 4

Find the Slope of a Parallel Line 9x+6y=-6

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