Chapter 6.5, Problem 43S

To determine

The inequality for the graph:

  

Answer to Problem 43S

The equality is $y+3x>-2$ .

Explanation of Solution

Given:

The graph is shown below:

  

Calculation:

Two of the coordinate of the line are (0, -2) and (-2, 4).

Slope of the line is calculated as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{4-\left(-2\right)}{-2-0}\\ =-3\end{array}$

Y-intercept is -2.

As the shaded area or solution of inequality is above to the line and the line is dashed then the inequality must be greater than.

The inequality of the graph is calculated as follows:

  $\begin{array}{l}y>mx+c\\ y>-3x+\left(-2\right)\\ y+3x>-2\end{array}$

Thus, the equality is $y+3x>-2$ .