Chapter 3.4, Problem 9E

To determine

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

$-4x+8y=-16$

Answer to Problem 9E

The x- intercept is at $x=4$ , and y -intercept is at $y=-2$ .

Explanation of Solution

Given:

$-4x+8y=-16$

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

$-4x+8y=-16$

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:

$\begin{array}{c}-4x+8\left(0\right)=-16\\ \Rightarrow -4x+0=-16\\ \Rightarrow -4x=-16\\ \Rightarrow x=\frac{-16}{-4}\\ \Rightarrow x=4\end{array}$

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

Putting $x=0$ in given equation:

$\begin{array}{c}-4\left(0\right)+8y=-16\\ \Rightarrow 0+8y=-16\\ \Rightarrow 8y=-16\\ \Rightarrow y=\frac{-16}{8}\\ \Rightarrow y=-2\end{array}$

Thus, x- and y -intercept of the graph of given equation are at points $x=4$ and $y=-2$ respectively.