Find the Slope and y-intercept 9x-3y=2

$9 x - 3 y = 2$

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 $9 x$ from both sides of the equation.

$- 3 y = 2 - 9 x$

Divide each term in $- 3 y = 2 - 9 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 2 - 9 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{2}{- 3} + \frac{- 9 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{2}{- 3} + \frac{- 9 x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{2}{- 3} + \frac{- 9 x}{- 3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{2}{3} + \frac{- 9 x}{- 3}$

Cancel the common factor of $- 9$ and $- 3$ .

Factor $- 3$ out of $- 9 x$ .

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

Cancel the common factors.

Factor $- 3$ out of $- 3$ .

$y = - \frac{2}{3} + \frac{- 3 (3 x)}{- 3 (1)}$

Cancel the common factor.

$y = - \frac{2}{3} + \frac{- 3 (3 x)}{- 3 \cdot 1}$

Rewrite the expression.

$y = - \frac{2}{3} + \frac{3 x}{1}$

Divide $3 x$ by $1$ .

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

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

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

Step 2

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

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

$m = 3$

$b = - \frac{2}{3}$

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

Slope: $3$

y-intercept: $(0, - \frac{2}{3})$

Slope: $3$

y-intercept: $(0, - \frac{2}{3})$

Step 3