Find the Slope of a Parallel Line 3+4x=2y-9

$3 + 4 x = 2 y - 9$

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.

$y = m x + b$

Rewrite the equation as $2 y - 9 = 3 + 4 x$ .

$2 y - 9 = 3 + 4 x$

Move all terms not containing $y$ to the right side of the equation.

Add $9$ to both sides of the equation.

$2 y = 3 + 4 x + 9$

Add $3$ and $9$ .

$2 y = 4 x + 12$

Divide each term in $2 y = 4 x + 12$ by $2$ and simplify.

Divide each term in $2 y = 4 x + 12$ by $2$ .

$\frac{2 y}{2} = \frac{4 x}{2} + \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{4 x}{2} + \frac{12}{2}$

Divide $y$ by $1$ .

$y = \frac{4 x}{2} + \frac{12}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

$y = \frac{2 (2 x)}{2} + \frac{12}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (2 x)}{2 (1)} + \frac{12}{2}$

Cancel the common factor.

$y = \frac{2 (2 x)}{2 \cdot 1} + \frac{12}{2}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{12}{2}$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{12}{2}$

Divide $12$ by $2$ .

$y = 2 x + 6$

Step 2

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

$m = 2$

Step 3

All lines that are parallel to $y = 2 x + 6$ have the same slope of $2$ .

$m_{parallel} = 2$

Step 4