Chapter 8.9, Problem 13E

To determine

To describe and correct:

The error in the graph of the given inequality.

Answer to Problem 13E

The correct shaded region will be the other side of the boundary line.

Explanation of Solution

Given:

An inequality and its graph: $y\le 2x+2$

  

Calculation:

Upon looking at our given inequality, we can see that it has a greater than or equal to sign. So the boundary line of our given inequality will be a solid line and the points on boundary line will be solution of the inequality.

To shade in the correct region, we will test point (0,0) in our given inequality as:

  $\begin{array}{l}y\le 2x+2\left(\text{Given inequality}\right)\\ 0\le 2(0)+2\left(\text{Substituting }x=0\text{}\text{ and }y=0\right)\\ 0\le 0+2\\ 0\le 2\end{array}$

Since the point satisfies our inequality, so we will shade in the region that includes point (0,0).

We can see from graph of given inequality that the shaded region doesn’t include point (0,0). The correct graph of our given inequality would look like: