Chapter 6.5, Problem 33PPE

To determine

To calculate: linear inequality that represents graph

Answer to Problem 33PPE

  $3x-2y<6$

Explanation of Solution

Given information:

  

Calculation:

The intersecting points are $A\left(x_1,y_1\right)=A\left(0,-3\right)$ and $B\left(x_2,y_2\right)=B\left(2,0\right)$

The equation of line when two points are given can be found out as:

  $\begin{array}{l}y-y_2=\frac{y_2-y_1}{x_2-x_1}\left(x-x_2\right)\\ y-0=\frac{0-\left(-3\right)}{2-0}\left(x-2\right)\\ y=\frac{3}{2}\left(x-2\right)\\ 2y=3x-6\\ 3x-2y=6\end{array}$

For forming the inequality,

For towards the origin, the condition should be true on putting $x=0$ and $y=0$

For away from the origin, the condition should be false on putting $x=0$ and $y=0$

Put $x=0$ and $y=0$ in $3x-2y=6$

  $\begin{array}{l}3\left(0\right)-2\left(0\right)=6\\ 0=6\end{array}$

As the graph is towards the origin that means condition should be true $0<6$

  $3x-2y<6$

We are taking $<$ not $\le$ , because the line is dashed

Graph: