Find the Slope of a Parallel Line 6y=-3x+5

$6 y = - 3 x + 5$

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.

$y = m x + b$

Divide each term in $6 y = - 3 x + 5$ by $6$ and simplify.

Divide each term in $6 y = - 3 x + 5$ by $6$ .

$\frac{6 y}{6} = \frac{- 3 x}{6} + \frac{5}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 3 x}{6} + \frac{5}{6}$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{6} + \frac{5}{6}$

Simplify the right side.

Simplify each term.

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

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

$y = \frac{3 (- x)}{6} + \frac{5}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$y = \frac{3 (- x)}{3 (2)} + \frac{5}{6}$

Cancel the common factor.

$y = \frac{3 (- x)}{3 \cdot 2} + \frac{5}{6}$

Rewrite the expression.

$y = \frac{- x}{2} + \frac{5}{6}$

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{5}{6}$

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

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{5}{6}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{5}{6}$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{2}$ .

$m = - \frac{1}{2}$

Step 3

All lines that are parallel to $y = - \frac{1}{2} x + \frac{5}{6}$ have the same slope of $- \frac{1}{2}$ .

$m_{parallel} = - \frac{1}{2}$

Step 4