Graph 2x-3y=6

$2 x - 3 y = 6$

Solve for $y$ .

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Subtract $2 x$ from both sides of the equation.

$- 3 y = 6 - 2 x$

Divide each term by $- 3$ and simplify.

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

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

Cancel the common factor of $- 3$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify each term.

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Divide $6$ by $- 3$ .

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

Dividing two negative values results in a positive value.

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

Rewrite in slope-intercept form.

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

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

Rewrite in slope-intercept form.

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

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

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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: $- 2$

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

y-intercept: $- 2$

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

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Choose $0$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $0$ in the expression.

$f (0) = \frac{2 (0)}{3} - 2$

Simplify the result.

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Multiply $2$ by $0$ .

$f (0) = \frac{0}{3} - 2$

Divide $0$ by $3$ .

$f (0) = 0 - 2$

Subtract $2$ from $0$ .

$f (0) = - 2$

The final answer is $- 2$ .

$- 2$

The $y$ value at $x = 0$ is $- 2$ .

$y = - 2$

Choose $3$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $3$ in the expression.

$f (3) = \frac{2 (3)}{3} - 2$

Simplify the result.

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Multiply $2$ by $3$ .

$f (3) = \frac{6}{3} - 2$

Divide $6$ by $3$ .

$f (3) = 2 - 2$

Subtract $2$ from $2$ .

$f (3) = 0$

The final answer is $0$ .

$0$

The $y$ value at $x = 3$ is $0$ .

$y = 0$

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

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

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

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

y-intercept: $- 2$

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

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