Find the Slope of a Parallel Line 6x+4y=7

$6 x + 4 y = 7$

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.

$4 y = 7 - 6 x$

Divide each term in $4 y = 7 - 6 x$ by $4$ and simplify.

Divide each term in $4 y = 7 - 6 x$ by $4$ .

$\frac{4 y}{4} = \frac{7}{4} + \frac{- 6 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{7}{4} + \frac{- 6 x}{4}$

Divide $y$ by $1$ .

$y = \frac{7}{4} + \frac{- 6 x}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6 x$ .

$y = \frac{7}{4} + \frac{2 (- 3 x)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{7}{4} + \frac{2 (- 3 x)}{2 (2)}$

Cancel the common factor.

$y = \frac{7}{4} + \frac{2 (- 3 x)}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{7}{4} + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = \frac{7}{4} - \frac{3 x}{2}$

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

Reorder $\frac{7}{4}$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} + \frac{7}{4}$

Reorder terms.

$y = - (\frac{3}{2} x) + \frac{7}{4}$

Remove parentheses.

$y = - \frac{3}{2} x + \frac{7}{4}$

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 $y = - \frac{3}{2} x + \frac{7}{4}$ have the same slope of $- \frac{3}{2}$ .

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

Step 4