Chapter 6.5, Problem 42S

To determine

The inequality for the graph:

  

Answer to Problem 42S

The equality is $y-x\ge -4$ .

Explanation of Solution

Given:

The graph is shown below:

  

Calculation:

Two of the coordinate of the line are (0, -4) and (4, 0).

Y-intercept of the line is -4.

Slope of the line is calculated as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{0-\left(-4\right)}{4-0}\\ =1\end{array}$

As the shaded area or solution of inequality is lower to the line and the line is solid then the inequality must be greater than equal to.

The inequality of the graph is calculated as follows:

  $\begin{array}{l}y\ge mx+c\\ y\ge \left(1\right)x+\left(-4\right)\\ y-x\ge -4\end{array}$

Thus, the equality is $y-x\ge -4$ .