Chapter 6.6, Problem 2LC

To determine

To write: a system of inequalities that represents the given graph.

Answer to Problem 2LC

  $\begin{array}{l}y-3x\ge 3\\ y+x<-2\end{array}$

Explanation of Solution

Given information: a figure is given as follows-

  

Since the dark line passes through the points (-1, 0)and (0, 3). So, its equation is

  $\begin{array}{l}\frac{y-0}{x+1}=\frac{3-0}{0-(-1)}=3\\ \Rightarrow \frac{y}{x+1}=3\\ \Rightarrow y=3x+3\\ \Rightarrow y-3x=3\end{array}$

This divides the xy-plane into two regions and two inequalities are possible such as $y-3x\ge 3$ and $y-3x\le 3$ .

Take any point from the colored region and put this value in the above inequalities which satisfies is the required inequality.

Such as take a point (-2, 2) from the colored region, the inequality which contains this point is $y-3x\ge 3$ . Hence this is the required inequality.

Similarly the other required inequality is $y+x<-2$ .