Find the Slope of a Parallel Line 8x-4y=1

$8 x - 4 y = 1$

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 $8 x$ from both sides of the equation.

$- 4 y = 1 - 8 x$

Divide each term in $- 4 y = 1 - 8 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 1 - 8 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{1}{- 4} + \frac{- 8 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{1}{- 4} + \frac{- 8 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{1}{- 4} + \frac{- 8 x}{- 4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{4} + \frac{- 8 x}{- 4}$

Cancel the common factor of $- 8$ and $- 4$ .

Factor $- 4$ out of $- 8 x$ .

$y = - \frac{1}{4} + \frac{- 4 (2 x)}{- 4}$

Cancel the common factors.

Factor $- 4$ out of $- 4$ .

$y = - \frac{1}{4} + \frac{- 4 (2 x)}{- 4 (1)}$

Cancel the common factor.

$y = - \frac{1}{4} + \frac{- 4 (2 x)}{- 4 \cdot 1}$

Rewrite the expression.

$y = - \frac{1}{4} + \frac{2 x}{1}$

Divide $2 x$ by $1$ .

$y = - \frac{1}{4} + 2 x$

Reorder $- \frac{1}{4}$ and $2 x$ .

$y = 2 x - \frac{1}{4}$

Step 2

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

$m = 2$

Step 3

All lines that are parallel to $y = 2 x - \frac{1}{4}$ have the same slope of $2$ .

$m_{parallel} = 2$

Step 4