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

$4 x + 2 y = 3$

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 $4 x$ from both sides of the equation.

$2 y = 3 - 4 x$

Divide each term in $2 y = 3 - 4 x$ by $2$ and simplify.

Divide each term in $2 y = 3 - 4 x$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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

Factor $2$ out of $- 4 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- 2 x$ by $1$ .

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

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

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

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

$m = - 2$

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

$m_{parallel} = - 2$