Graph y=1/3f(x+5)-3

$y = \frac{1}{3} f (x + 5) - 3$

Step 1

Solve for $y$ .

Remove parentheses.

$y = \frac{1}{3} \cdot (f (x + 5)) - 3$

Remove parentheses.

$y = \frac{1}{3} \cdot (f (x + 5)) - 3$

Simplify each term.

Apply the distributive property.

$y = \frac{1}{3} \cdot (f x + f \cdot 5) - 3$

Move $5$ to the left of $f$ .

$y = \frac{1}{3} \cdot (f x + 5 \cdot f) - 3$

Apply the distributive property.

$y = \frac{1}{3} (f x) + \frac{1}{3} (5 f) - 3$

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

Combine $f$ and $\frac{1}{3}$ .

$y = \frac{f}{3} x + \frac{1}{3} (5 f) - 3$

Combine $\frac{f}{3}$ and $x$ .

$y = \frac{f x}{3} + \frac{1}{3} (5 f) - 3$

Multiply $\frac{1}{3} (5 f)$ .

Combine $5$ and $\frac{1}{3}$ .

$y = \frac{f x}{3} + \frac{5}{3} f - 3$

Combine $\frac{5}{3}$ and $f$ .

$y = \frac{f x}{3} + \frac{5 f}{3} - 3$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Combine $\frac{5 f}{3} - 3$ .

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{f x}{3} + \frac{5 f}{3} - 3 \cdot \frac{3}{3}$

Combine $- 3$ and $\frac{3}{3}$ .

$y = \frac{f x}{3} + \frac{5 f}{3} + \frac{- 3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{f x}{3} + \frac{5 f - 3 \cdot 3}{3}$

Multiply $- 3$ by $3$ .

$y = \frac{f x}{3} + \frac{5 f - 9}{3}$

Rewrite in slope-intercept form.

$y = \frac{x}{3} f + \frac{5 f - 9}{3}$

Step 3

The slope and y-intercept cannot be found for this problem since it is not linear.

Not Linear

Step 4

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

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

$m =$

$b =$

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

Slope:

y-intercept: $(0,)$

Slope:

y-intercept: $(0,)$

Step 5

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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

$\begin{array}{c} x & y \\ 0 & - 3 + \frac{5 f}{3} \\ 1 & - 3 + 2 f \end{array}$

Step 6

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

Slope:

y-intercept: $(0,)$

$\begin{array}{c} x & y \\ 0 & - 3 + \frac{5 f}{3} \\ 1 & - 3 + 2 f \end{array}$

Step 7

Graph y=1/3f(x+5)-3

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