Find the Slope and y-intercept 5x-6y=12

$5 x - 6 y = 12$

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 $5 x$ from both sides of the equation.

$- 6 y = 12 - 5 x$

Divide each term in $- 6 y = 12 - 5 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 12 - 5 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 6$ .

$y = - 2 + \frac{- 5 x}{- 6}$

Dividing two negative values results in a positive value.

$y = - 2 + \frac{5 x}{6}$

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

Reorder $- 2$ and $\frac{5 x}{6}$ .

$y = \frac{5 x}{6} - 2$

Reorder terms.

$y = \frac{5}{6} x - 2$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{5}{6}$

$b = - 2$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{5}{6}$

y-intercept: $(0, - 2)$

Slope: $\frac{5}{6}$

y-intercept: $(0, - 2)$

Step 3