Algebra Examples

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

Step 1

Graph $2 x + y = 2$ .

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Step 1.1

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

$y = 2 - 2 x$

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 $2$ and $- 2 x$ .

$y = - 2 x + 2$

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 $y = m x + b$ .

$m = - 2$

$b = 2$

Step 1.3.2

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

Slope: $- 2$

y-intercept: $(0, 2)$

Slope: $- 2$

y-intercept: $(0, 2)$

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

Reorder $2$ and $- 2 x$ .

$y = - 2 x + 2$

Step 1.4.2

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

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

Step 1.5

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

Slope: $- 2$

y-intercept: $(0, 2)$

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

Slope: $- 2$

y-intercept: $(0, 2)$

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

Step 2

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

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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.

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

Step 2.1.2.2

Remove parentheses.

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

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 $y = m x + b$ .

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

$b = - 3$

Step 2.2.2

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

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

y-intercept: $(0, - 3)$

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

y-intercept: $(0, - 3)$

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.

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

Step 2.3.1.2

Remove parentheses.

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

Step 2.3.2

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

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

Step 2.4

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

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

y-intercept: $(0, - 3)$

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

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

y-intercept: $(0, - 3)$

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

Step 3

Plot each graph on the same coordinate system.

$2 x + y = 2$

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

Step 4