Chapter 8.2, Problem 30E

To determine

To write:

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

Answer to Problem 30E

The function form of our given equation would be $y=\frac{5}{2}x-3$ .

Explanation of Solution

Given:

An equation: $5x-2y=6$

Calculation:

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

  $\begin{array}{l}5x-2y=6\left(\text{Given equation}\right)\\ 5x-5x-2y=6-5x\left(\text{Subtracting 5}x\text{ from both sides}\right)\\ -2y=-5x+6\\ \frac{-2y}{-2}=\frac{-5x}{-2}+\frac{6}{-2}\left(\text{Dividing both sides by }-2\right)\\ y=\frac{5}{2}x-3\end{array}$

Therefore, the function form of our given equation would be $y=\frac{5}{2}x-3$ .

We can see that the slope of our given equation is $\frac{5}{2}$ and the y -intercept is $(0,-3)$ .

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