Algebra Examples

$g (x) = \frac{1}{3} f (x) - 2$

Step 1

Rewrite the function as an equation.

$y = \frac{1}{3} \cdot f (x) - 2$

Step 2

Combine $\frac{1}{3}$ and $f (x)$ .

$y = \frac{f (x)}{3} - 2$

Step 3

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

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Step 3.1

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 3.2

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

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

$b = - 2$

Step 3.3

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: $(0, - 2)$

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

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

Step 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 4.1

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

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & \frac{f}{3} - 2 \end{array}$

Step 5

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

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

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

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & \frac{f}{3} - 2 \end{array}$

Step 6