Find the Slope of a Parallel Line 15x-16y=1

$15 x - 16 y = 1$

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 $15 x$ from both sides of the equation.

$- 16 y = 1 - 15 x$

Divide each term in $- 16 y = 1 - 15 x$ by $- 16$ and simplify.

Divide each term in $- 16 y = 1 - 15 x$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{1}{- 16} + \frac{- 15 x}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{1}{- 16} + \frac{- 15 x}{- 16}$

Divide $y$ by $1$ .

$y = \frac{1}{- 16} + \frac{- 15 x}{- 16}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{16} + \frac{- 15 x}{- 16}$

Dividing two negative values results in a positive value.

$y = - \frac{1}{16} + \frac{15 x}{16}$

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

Reorder $- \frac{1}{16}$ and $\frac{15 x}{16}$ .

$y = \frac{15 x}{16} - \frac{1}{16}$

Reorder terms.

$y = \frac{15}{16} x - \frac{1}{16}$

Step 2

Using the slope-intercept form, the slope is $\frac{15}{16}$ .

$m = \frac{15}{16}$

Step 3

All lines that are parallel to $y = \frac{15}{16} x - \frac{1}{16}$ have the same slope of $\frac{15}{16}$ .

$m_{parallel} = \frac{15}{16}$

Step 4