Algebra Examples

$x + 3 y = 9$ $y = \frac{4}{3} x - 2$

Step 1

Graph $x + 3 y = 9$ .

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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.

$3 y = 9 - x$

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $3$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

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

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 $9$ by $3$ .

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

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

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

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

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

Step 1.2.3

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

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Step 1.2.3.1

Reorder terms.

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

Step 1.2.3.2

Remove parentheses.

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

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 $y = m x + b$ .

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

$b = 3$

Step 1.3.2

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

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

y-intercept: $(0, 3)$

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

y-intercept: $(0, 3)$

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

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

Step 1.4.1.2

Reorder terms.

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

Step 1.4.1.3

Remove parentheses.

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

Step 1.4.2

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

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

Step 1.5

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

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

y-intercept: $(0, 3)$

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

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

y-intercept: $(0, 3)$

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

Step 2

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

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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

Reorder terms.

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

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 $y = m x + b$ .

$m = \frac{4}{3}$

$b = - 2$

Step 2.2.2

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

Slope: $\frac{4}{3}$

y-intercept: $(0, - 2)$

Slope: $\frac{4}{3}$

y-intercept: $(0, - 2)$

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

Reorder terms.

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

Step 2.3.2

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

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

Step 2.4

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

Slope: $\frac{4}{3}$

y-intercept: $(0, - 2)$

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

Slope: $\frac{4}{3}$

y-intercept: $(0, - 2)$

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

Step 3

Plot each graph on the same coordinate system.

$x + 3 y = 9$

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

Step 4