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Chapter 4: Q. 511 (page 556)

Write the inequality shown by the graph with the boundary line y=2x - 4.

Short Answer

Expert verified

y<2x-4

Step by step solution

01

Step 1. Given information 

We have been given a graph.

We have to write the inequality shown by the graph.

02

Step 2. Find the inequality representing the shaded region

The line y=2x-4is the boundary line.

On one side of the line are the points with y > 2x - 4 and on the other side of the line are the points with y < 2x - 4 .

Let鈥檚 test the point (0, 0) and see which inequality describes its side of the boundary line.

At (0, 0) , which inequality is true:

y>2x-40>?2(0)-40>-4 or y<2x-40<?2(0)-40鈮�-4

So the side with (0, 0) is the side where y > 2x - 4 .

We need to find the inequality for the region that does not contain (0,0).

Since the boundary line is graphed as a dashed line, the inequality does not include an equal sign.

The graph shows the solution to the inequality y < 2x - 4.

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