Find the Slope 3x-8y=16

$3 x - 8 y = 16$

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 $3 x$ from both sides of the equation.

$- 8 y = 16 - 3 x$

Divide each term in $- 8 y = 16 - 3 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 16 - 3 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{16}{- 8} + \frac{- 3 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{16}{- 8} + \frac{- 3 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{16}{- 8} + \frac{- 3 x}{- 8}$

Simplify the right side.

Simplify each term.

Divide $16$ by $- 8$ .

$y = - 2 + \frac{- 3 x}{- 8}$

Dividing two negative values results in a positive value.

$y = - 2 + \frac{3 x}{8}$

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

Reorder $- 2$ and $\frac{3 x}{8}$ .

$y = \frac{3 x}{8} - 2$

Reorder terms.

$y = \frac{3}{8} x - 2$

Step 2

Using the slope-intercept form, the slope is $\frac{3}{8}$ .

$m = \frac{3}{8}$

Step 3