Chapter 8.2, Problem 29E

To determine

To write:

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

Answer to Problem 29E

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

Explanation of Solution

Given:

An equation: $3x+4y=0$

Calculation:

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

  $\begin{array}{l}3x+4y=0\left(\text{Given equation}\right)\\ 3x-3x+4y=0-3x\left(\text{Subtracting 3}x\text{ from both sides}\right)\\ 4y=-3x\\ \frac{4y}{4}=-\frac{3x}{4}\left(\text{Dividing both sides by }4\right)\\ y=-\frac{3}{4}x\end{array}$

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

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

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