Chapter 3.4, Problem 12E

To determine

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

$-x+8y=4$

Answer to Problem 12E

The x- intercept is at $x=-4$ , and y -intercept is at $y=0.5$ .

Explanation of Solution

Given:

$-x+8y=4$

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

$-x+8y=4$

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:

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

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

Putting $x=0$ in given equation:

  $\begin{array}{c}-\left(0\right)+8y=4\\ \Rightarrow 0+8y=4\\ \Rightarrow 8y=4\\ \Rightarrow y=\frac{4}{8}\\ \Rightarrow y=0.5\end{array}$

Thus, x- and y -intercept of the graph of given equation are at points $x=-4$ and $y=0.5$ respectively.