Algebra Examples

$f (x) = x$ $g (x) = x + 5$

Step 1

Graph $f (x) = x$ .

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Step 1.1

Rewrite the function as an equation.

$y = x$

Step 1.2

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

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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

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

$m = 1$

$b = 0$

Step 1.2.3

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

Slope: $1$

y-intercept: $(0, 0)$

Slope: $1$

y-intercept: $(0, 0)$

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

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

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

Step 1.4

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

Slope: $1$

y-intercept: $(0, 0)$

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

Slope: $1$

y-intercept: $(0, 0)$

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

Step 2

Graph $g (x) = x + 5$ .

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Step 2.1

Rewrite the function as an equation.

$y = x + 5$

Step 2.2

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

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Step 2.2.1

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 2.2.2

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

$m = 1$

$b = 5$

Step 2.2.3

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

Slope: $1$

y-intercept: $(0, 5)$

Slope: $1$

y-intercept: $(0, 5)$

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

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

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 6 \end{array}$

Step 2.4

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

Slope: $1$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 6 \end{array}$

Slope: $1$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 6 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$f (x) = x$

$g (x) = x + 5$

Step 4