Chapter 8.2, Problem 10C

To determine

To write:

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

Answer to Problem 10C

The function form of our given equation would be $y=\frac{2}{3}x-1$ .

Explanation of Solution

Given:

An equation: $2x-3y=3$

Calculation:

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

  $\begin{array}{l}2x-3y=3\left(\text{Given equation}\right)\\ 2x-2x-3y=3-2x\left(\text{Subtracting }2x\text{ from both sides}\right)\\ -3y=-2x+3\\ \frac{-3y}{-3}=\frac{-2x}{-3}+\frac{3}{-3}\left(\text{Dividing both sides by }-3\right)\\ y=\frac{2}{3}x-1\end{array}$

Therefore, the function form of our given equation would be $y=\frac{2}{3}x-1$ .

We can see that the slope of our given equation is $\frac{2}{3}$ and the y -intercept is $(0,-1)$ .

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