Algebra Examples

$y = - \frac{1}{2} x - 1$ and $y = \frac{1}{4} x - 4$

Step 1

Graph $y = - \frac{1}{2} x - 1$ .

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Step 1.1

Rewrite in slope-intercept form.

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Step 1.1.1

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 1.1.2

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

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Step 1.1.2.1

Reorder terms.

$y = - (\frac{1}{2} x) - 1$

Step 1.1.2.2

Remove parentheses.

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

Step 1.2

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

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Step 1.2.1

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

$m = - \frac{1}{2}$

$b = - 1$

Step 1.2.2

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

Slope: $- \frac{1}{2}$

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

Slope: $- \frac{1}{2}$

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

Step 1.3

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 1.3.1

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

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Step 1.3.1.1

Reorder terms.

$y = - (\frac{1}{2} x) - 1$

Step 1.3.1.2

Remove parentheses.

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

Step 1.3.2

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

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

Step 1.4

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

Slope: $- \frac{1}{2}$

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

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

Slope: $- \frac{1}{2}$

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

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

Step 2

Graph $y = \frac{1}{4} x - 4$ .

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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

Reorder terms.

$y = \frac{1}{4} x - 4$

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 $y = m x + b$ .

$m = \frac{1}{4}$

$b = - 4$

Step 2.2.2

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

Slope: $\frac{1}{4}$

y-intercept: $(0, - 4)$

Slope: $\frac{1}{4}$

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

Reorder terms.

$y = \frac{1}{4} x - 4$

Step 2.3.2

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

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

Step 2.4

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

Slope: $\frac{1}{4}$

y-intercept: $(0, - 4)$

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

Slope: $\frac{1}{4}$

y-intercept: $(0, - 4)$

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

Step 3

Plot each graph on the same coordinate system.

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

$y = \frac{1}{4} x - 4$

Step 4