Chapter 4: Q. 4.140 (page 548)

Write the inequality shown by the graph with the boundary line $y = \frac{1}{2} x - 4$

Short Answer

Expert verified

The inequality shown by the graph is $y \leq \frac{1}{2} x - 4$ .

Step by step solution

Step 1. Given Information

We are given an equation $y = \frac{1}{2} x - 4$ and a graph,

Step 2. Finding the inequality

The line $y = \frac{1}{2} x - 4$ is the boundary line. On one side of the line are the points with $y > \frac{1}{2} x - 4$ and on the other side of the line are the points with $y = \frac{1}{2} x - 4$ .

Checking the inequality with point $(0, 0)$ ,

$y > \frac{1}{2} x - 4 0 > \frac{1}{2} (0) - 4 0 > - 4$

True.

Step 3. Finding the inequality

Checking the inequality with point $(0, 0)$ ,

role="math" $y < \frac{1}{2} x - 4 0 < \frac{1}{2} (0) - 4 0 < - 4$

False.

Since $y > \frac{1}{2} x - 4$ is true for $(0, 0)$ , which is not the part of shaded region, hence shaded region is the solution for the other inequality $y < \frac{1}{2} x - 4$

Also, the boundary line is graphed with a solid line, the inequality includes the equal sign.

$y \leq \frac{1}{2} x - 4$

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Write the inequality shown by the graph with the boundary line $y = \frac{1}{2} x - 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

Step 3. Finding the inequality

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Write the inequality shown by the graph with the boundary line $y = \frac{1}{2} x - 4$