Graph 3x-9y=9

$3 x - 9 y = 9$

Step 1

Solve for $y$ .

Subtract $3 x$ from both sides of the equation.

$- 9 y = 9 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $9$ by $- 9$ .

$y = - 1 + \frac{- 3 x}{- 9}$

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

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

$y = - 1 + \frac{- 3 (x)}{- 9}$

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Reorder terms.

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

Step 3

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

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

$m = \frac{1}{3}$

$b = - 1$

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

Slope: $\frac{1}{3}$

y-intercept: $(0, - 1)$

Slope: $\frac{1}{3}$

y-intercept: $(0, - 1)$

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.

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

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

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

Reorder terms.

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

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

$\begin{array}{c} x & y \\ 0 & - 1 \\ 3 & 0 \end{array}$

Step 5

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

Slope: $\frac{1}{3}$

y-intercept: $(0, - 1)$

$\begin{array}{c} x & y \\ 0 & - 1 \\ 3 & 0 \end{array}$

Step 6

Graph 3x-9y=9

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