Graph 2x-6y=30 y=1/3x+1

$2 x - 6 y = 30$ $y = \frac{1}{3} x + 1$

Step 1

Graph $2 x - 6 y = 30$ .

Solve for $y$ .

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

$- 6 y = 30 - 2 x$

Divide each term in $- 6 y = 30 - 2 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 30 - 2 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{30}{- 6} + \frac{- 2 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{30}{- 6} + \frac{- 2 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{30}{- 6} + \frac{- 2 x}{- 6}$

Simplify the right side.

Simplify each term.

Divide $30$ by $- 6$ .

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

Cancel the common factor of $- 2$ and $- 6$ .

Factor $- 2$ out of $- 2 x$ .

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

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = - 5 + \frac{- 2 (x)}{- 2 (3)}$

Cancel the common factor.

$y = - 5 + \frac{- 2 x}{- 2 \cdot 3}$

Rewrite the expression.

$y = - 5 + \frac{x}{3}$

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 $- 5$ and $\frac{x}{3}$ .

$y = \frac{x}{3} - 5$

Reorder terms.

$y = \frac{1}{3} x - 5$

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

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

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

$b = - 5$

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: $(0, - 5)$

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

y-intercept: $(0, - 5)$

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 $- 5$ and $\frac{x}{3}$ .

$y = \frac{x}{3} - 5$

Reorder terms.

$y = \frac{1}{3} x - 5$

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

$\begin{array}{c} x & y \\ 0 & - 5 \\ 3 & - 4 \end{array}$

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

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

y-intercept: $(0, - 5)$

$\begin{array}{c} x & y \\ 0 & - 5 \\ 3 & - 4 \end{array}$

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

y-intercept: $(0, - 5)$

$\begin{array}{c} x & y \\ 0 & - 5 \\ 3 & - 4 \end{array}$

Step 2

Graph $y = \frac{1}{3} x + 1$ .

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.

$y = m x + b$

Reorder terms.

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

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: $(0, 1)$

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.

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

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

$\begin{array}{c} x & y \\ 0 & 1 \\ 3 & 2 \end{array}$

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

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

y-intercept: $(0, 1)$

$\begin{array}{c} x & y \\ 0 & 1 \\ 3 & 2 \end{array}$

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

y-intercept: $(0, 1)$

$\begin{array}{c} x & y \\ 0 & 1 \\ 3 & 2 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$2 x - 6 y = 30$

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

Step 4

Graph 2x-6y=30 y=1/3x+1

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