Find the Slope of a Parallel Line 7x-y=5

$7 x - y = 5$

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.

$y = m x + b$

Subtract $7 x$ from both sides of the equation.

$- y = 5 - 7 x$

Divide each term in $- y = 5 - 7 x$ by $- 1$ and simplify.

Divide each term in $- y = 5 - 7 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{5}{- 1} + \frac{- 7 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{5}{- 1} + \frac{- 7 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{5}{- 1} + \frac{- 7 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $5$ by $- 1$ .

$y = - 5 + \frac{- 7 x}{- 1}$

Move the negative one from the denominator of $\frac{- 7 x}{- 1}$ .

$y = - 5 - 1 \cdot (- 7 x)$

Rewrite $- 1 \cdot (- 7 x)$ as $- (- 7 x)$ .

$y = - 5 - (- 7 x)$

Multiply $- 7$ by $- 1$ .

$y = - 5 + 7 x$

Reorder $- 5$ and $7 x$ .

$y = 7 x - 5$

Step 2

Using the slope-intercept form, the slope is $7$ .

$m = 7$

Step 3

All lines that are parallel to $y = 7 x - 5$ have the same slope of $7$ .

$m_{parallel} = 7$

Step 4