Chapter 8, Problem 6MCQ

To determine

To graph:

The given equations. Tell whether each equation is a function.

Answer to Problem 6MCQ

The equation $x+4y=32$ is a function.

Explanation of Solution

Given:

An equation:

  $x+4y=32$

Concept used:

We know that slope-intercept form of equation is $y=mx+b$ , where m represents slope of line and b represents the y-intercept.

Calculation:

First of all, we will convert our given equation in slope-intercept form as:

  $\begin{array}{l}x+4y=32\left(\text{Given equation}\right)\\ x-x+4y=32-x\left(\text{Subtracting }x\text{ from both sides}\right)\\ 4y=-x+32\\ \frac{4y}{4}=\frac{-x}{4}+\frac{32}{4}\\ y=-\frac{1}{4}x+8\end{array}$

Upon looking at our given equation, we can see that the slope of our given line is $-\frac{1}{4}$ and the y-intercept is at point $\left(0,8\right)$ .

Upon graphing $x+4y=32$ , we will get our required graph as shown below:

  

We can see that no vertical line will intersect the graph of equation $x+4y=32$ more than one place that is each x value corresponds to a specific y-value.

Therefore, the equation $x+4y=32$ is a function.