Chapter 6.5, Problem 4LC

To determine

To write: The inequality representation of the given graph.

Explanation of Solution

Given information:

The given graph is as follows:

  

Formula used:

The equation of the line passing through the points $(x_1,y_1)\&(x_2,y_2)$ is

  $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

From the given graph,

The boundary line is passing through the points $(2,0)\&(0,-1)$

The equation of the line is

  $\begin{array}{l}\frac{y-0}{x-2}=\frac{-1-0}{0-2}\\ \frac{y}{x-2}=\frac{-1}{-2}\\ -2y=-1(x-2)\\ 2y=x-2\\ y=\frac{1}{2}x-1\end{array}$

The boundary line is dashed line.

The shaded region is the below the boundary line.

Hence, the inequality representation of the given graph is $y<\frac{1}{2}x-1$ .