Graph 2x-6=3y

$2 x - 6 = 3 y$

Step 1

Solve for $y$ .

Rewrite the equation as $3 y = 2 x - 6$ .

$3 y = 2 x - 6$

Divide each term in $3 y = 2 x - 6$ by $3$ and simplify.

Divide each term in $3 y = 2 x - 6$ by $3$ .

$\frac{3 y}{3} = \frac{2 x}{3} + \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{2 x}{3} + \frac{- 6}{3}$

Divide $y$ by $1$ .

$y = \frac{2 x}{3} + \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

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

Step 2

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.

$y = m x + b$

Reorder terms.

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

Step 3

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

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

$m = \frac{2}{3}$

$b = - 2$

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

Slope: $\frac{2}{3}$

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

Slope: $\frac{2}{3}$

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

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder terms.

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

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 2 \\ 3 & 0 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{2}{3}$

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

$\begin{array}{c} x & y \\ 0 & - 2 \\ 3 & 0 \end{array}$

Step 6