Chapter 3.4, Problem 8E

To determine

To determine x- and y -intercept of the graph of linear equation

$3x+6y=24$

Answer to Problem 8E

The x- intercept is at $x=8$ , and y -intercept is at $y=4$

Explanation of Solution

Given:

$3x+6y=24$

Concept Used:

To find x -intercept of graph of a equation find the x coordinate when $y=0$ .

To find y -intercept of graph of a equation find the y coordinate when $x=0$ .

Calculation:

In order to determine x- and y -intercept of the graph of linear equation

$3x+6y=24$

First, let’s find x -intercept of graph of above equation by finding the x coordinate when $y=0$ .

Putting $y=0$ in given equation:

$\begin{array}{c}3x+6\left(0\right)=24\\ \Rightarrow 3x+0=24\\ \Rightarrow 3x=24\\ \Rightarrow x=\frac{24}{3}\\ \Rightarrow x=8\end{array}$

Now, to find y -intercept of graph of above equation by finding the y coordinate when $x=0$ .

Putting $x=0$ in given equation:

$\begin{array}{c}3\left(0\right)+6y=24\\ \Rightarrow 0+6y=24\\ \Rightarrow 6y=24\\ \Rightarrow y=\frac{24}{6}\\ \Rightarrow y=4\end{array}$

Thus, x- and y -intercept of the graph of given equation are at points $x=8$ and $y=4$ respectively.