Algebra Examples

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

Step 1

Graph $x - 6 y = 6$ .

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Subtract $x$ from both sides of the equation.

$- 6 y = 6 - x$

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 6$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $6$ by $- 6$ .

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

Step 1.1.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.2

Rewrite in slope-intercept form.

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Step 1.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2.2

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

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

Step 1.2.3

Reorder terms.

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

Step 1.3

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

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Step 1.3.1

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

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

$b = - 1$

Step 1.3.2

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: $(0, - 1)$

Step 1.4

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

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Step 1.4.1

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

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Step 1.4.1.1

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

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

Step 1.4.1.2

Reorder terms.

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

Step 1.4.2

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

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

Step 1.5

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: $(0, - 1)$

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

Step 2

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

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.1.2

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

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Step 2.1.2.1

Reorder terms.

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

Step 2.1.2.2

Remove parentheses.

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

Step 2.2

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

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Step 2.2.1

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

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

$b = 4$

Step 2.2.2

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: $(0, 4)$

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

y-intercept: $(0, 4)$

Step 2.3

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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Step 2.3.1

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

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Step 2.3.1.1

Reorder terms.

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

Step 2.3.1.2

Remove parentheses.

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

Step 2.3.2

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

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

Step 2.4

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: $(0, 4)$

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

Step 3

Plot each graph on the same coordinate system.

$x - 6 y = 6$

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

Step 4