Find the Slope 3x-5y=1

$3 x - 5 y = 1$

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 $3 x$ from both sides of the equation.

$- 5 y = 1 - 3 x$

Divide each term in $- 5 y = 1 - 3 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 1 - 3 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{1}{- 5} + \frac{- 3 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{1}{- 5} + \frac{- 3 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{1}{- 5} + \frac{- 3 x}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{5} + \frac{- 3 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{1}{5} + \frac{3 x}{5}$

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

Reorder $- \frac{1}{5}$ and $\frac{3 x}{5}$ .

$y = \frac{3 x}{5} - \frac{1}{5}$

Reorder terms.

$y = \frac{3}{5} x - \frac{1}{5}$

Step 2

Using the slope-intercept form, the slope is $\frac{3}{5}$ .

$m = \frac{3}{5}$

Step 3