Algebra Examples

$f (x) = 2$ if $x = 1$

Step 1

Graph $f (x) = 2$ .

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Step 1.1

Rewrite the function as an equation.

$y = 2$

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 $y = m x + b$ .

$m = 0$

$b = 2$

Step 1.2.3

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

Slope: $0$

y-intercept: $(0, 2)$

Slope: $0$

y-intercept: $(0, 2)$

Step 1.3

Find two points on the line.

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

Step 1.4

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

Slope: $0$

y-intercept: $(0, 2)$

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

Slope: $0$

y-intercept: $(0, 2)$

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

Step 2

Graph $x = 1$ .

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Step 2.1

Since $x = 1$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 2.2

Find two points on the line.

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

Step 2.3

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

Slope: Undefined

y-intercept: No y-intercept

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

Slope: Undefined

y-intercept: No y-intercept

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

Step 3

Plot each graph on the same coordinate system.

$f (x) = 2$

$x = 1$

Step 4