Graph x-6y=6 y=-2/3x+4

$x - 6 y = 6$ $y = - \frac{2}{3} x + 4$

Graph $x - 6 y = 6$ .

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$- 6 y = 6 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $6$ by $- 6$ .

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

Dividing two negative values results in a positive value.

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

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 $\frac{x}{6}$ .

$y = \frac{x}{6} - 1$

Reorder terms.

$y = \frac{1}{6} x - 1$

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

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

$m = \frac{1}{6}$

$b = - 1$

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

Slope: $\frac{1}{6}$

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

Slope: $\frac{1}{6}$

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.

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

Reorder $- 1$ and $\frac{x}{6}$ .

$y = \frac{x}{6} - 1$

Reorder terms.

$y = \frac{1}{6} x - 1$

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

$\begin{array}{c} x & y \\ 0 & - 1 \\ 6 & 0 \end{array}$

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

Slope: $\frac{1}{6}$

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

$\begin{array}{c} x & y \\ 0 & - 1 \\ 6 & 0 \end{array}$

Slope: $\frac{1}{6}$

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

$\begin{array}{c} x & y \\ 0 & - 1 \\ 6 & 0 \end{array}$

Graph $y = - \frac{2}{3} x + 4$ .

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.

$y = m x + b$

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

Reorder terms.

$y = - (\frac{2}{3} x) + 4$

Remove parentheses.

$y = - \frac{2}{3} x + 4$

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

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

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

$b = 4$

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: $(0, 4)$

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

y-intercept: $(0, 4)$

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 terms.

$y = - (\frac{2}{3} x) + 4$

Remove parentheses.

$y = - \frac{2}{3} x + 4$

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

$\begin{array}{c} x & y \\ 0 & 4 \\ 3 & 2 \end{array}$

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

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

y-intercept: $(0, 4)$

$\begin{array}{c} x & y \\ 0 & 4 \\ 3 & 2 \end{array}$

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

y-intercept: $(0, 4)$

$\begin{array}{c} x & y \\ 0 & 4 \\ 3 & 2 \end{array}$

Plot each graph on the same coordinate system.

$x - 6 y = 6$

$y = - \frac{2}{3} x + 4$

Graph x-6y=6 y=-2/3x+4

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