Chapter 5.6, Problem 40HP

To determine

To summarize: the steps and to graph an inequality in two variables.

Explanation of Solution

There are three steps

1. Rearrange the equation so $y$ is on the left and everything else on the right.
2. Plot the $y=$ line (make it a solid line for  $y\le$  or $y\ge$ , and a dashed line for $y<\text{or}y>$ .
3. Shade above the line for a greater than $\left(y>\text{or}y\ge \right)$ or below the line for a less than $\left(y<\text{or}y\le \right)$ .

Example: $y\le 2x-1$

1. The inequality already has y on the left and everything else on the right, so no need to rearrange

2. Plot  $y=2x-1$  (as a solid line because $y\le$ includes equal to)

  

4. Shade the area below (because $y$ is less than or equal to)