Chapter 8.9, Problem 14E

To determine

When graphing the inequality $y\ge 2x$ , can you use (0,0) as a test point to determine which side of the boundary to shade? Explain.

Answer to Problem 14E

We cannot use (0,0) as a test point to determine which side of the boundary to shade for inequality $y\ge 2x$ .

Explanation of Solution

Given:

An inequality:

  $y\le 2x$ .

Calculation:

First of all, we need to draw the boundary line while graphing an inequality.

To draw the boundary line of an inequality, we simply replace the inequality signs $\left(>,<,\le ,\ge \right)$ by equal to sign.

The boundary line of inequality $y\le 2x$ would be $y=2x$ . After drawing boundary line, we will shade in the correct region.

To shade in the correct region, we will choose a test point which is not on boundary line. If the test point satisfies the inequality, then we will shade in the part which includes test point.

If the test point doesn’t satisfy the inequality, then we will shade in the part which excludes test point.

We can see that boundary line of our inequality will pass through the origin (0,0). Since (0,0) in on boundary line, so it will not tell which side of boundary line we should shade in.

Therefore, wecannot use (0,0) as a test point to determine which side of the boundary to shade for inequality $y\ge 2x$ .