Chapter 7, Problem 6STP

To determine

To find: The inequality shown in given graph.

Answer to Problem 6STP

The inequality shown in graph is $y\le \frac{2x-3}{-3}$ .

Explanation of Solution

Given information:

The given graph is shown in figure $\left(1\right)$ .

  

figure $\left(1\right)$ .

Calculation:

  

Figure- $\left(1\right)$ .

If we look at figure $\left(1\right)$ , it is clear that it passes through $\left(0,1\right)$ and $\left(-3,3\right)$ .

Equation of line passes through $\left(0,1\right)$ and $\left(-3,3\right)$ is to be found.

So we have $\left(x_1,y_1\right)=\left(0,1\right)$ and $\left(x_2,y_2\right)=\left(-3,3\right)$

Comparing we get $x_1=0,y_1=1,x_2=-3,y_2=3$

Put values of $x_1,y_1,x_2,y_2$ in given equation.

Equation of the required line is;

  $\begin{array}{c}y-1=\frac{3-1}{-3-0}\left(x-0\right)\\ y-1=\frac{2}{-3}\left(x-0\right)\\ -3\left(y-1\right)=2x\\ -3y+3=2x\end{array}$

  $\begin{array}{c}-3y=2x-3\\ y\le \frac{2x-3}{-3}\end{array}$

Therefore, The inequality shown in graph is $y\le \frac{2x-3}{-3}$ .