Chapter 8.2, Problem 31E

To determine

To write:

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

Answer to Problem 31E

The function form of our given equation would be $y=-\frac{2}{3}x+4$ .

Explanation of Solution

Given:

An equation: $2x+3y=12$

Calculation:

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

  $\begin{array}{l}2x+3y=12\left(\text{Given equation}\right)\\ 2x-2x+3y=12-2x\left(\text{Subtracting 2}x\text{ from both sides}\right)\\ 3y=-2x+12\\ \frac{3y}{3}=\frac{-2x}{3}+\frac{12}{3}\left(\text{Dividing both sides by }3\right)\\ y=-\frac{2}{3}x+4\end{array}$

Therefore, the function form of our given equation would be $y=-\frac{2}{3}x+4$ .

We can see that the slope of our given equation is $-\frac{2}{3}$ and the y -intercept is $(0,4)$ .

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