Chapter 8.2, Problem 28E

To determine

To write:

The given equation in function form.Then graph the equation.

Answer to Problem 28E

The function form of our given equation would be $y=\frac{1}{3}x+3$ .

Explanation of Solution

Given:

An equation: $x-3y=-9$

Calculation:

To write the given equation in function form, we need to convert our equation in slope-intercept form $(y=mx+b)$ as:

  $\begin{array}{l}x-3y=-9\left(\text{Given equation}\right)\\ x-x-3y=-9-x\left(\text{Subtracting }x\text{ from both sides}\right)\\ -3y=-x-9\\ \frac{-3y}{-3}=\frac{-x}{-3}-\frac{9}{-3}\left(\text{Dividing both sides by }-3\right)\\ y=\frac{1}{3}x+3\end{array}$

Therefore, the function form of our given equation would be $y=\frac{1}{3}x+3$ .

We can see that the slope of our given equation is $\frac{1}{3}$ and the y -intercept is $(0,3)$ .

Upon graphing our given equation, we will get our required graph as shown below: