Chapter 12, Problem 12CCSR

To determine

To find: the linear inequality that describes the graph given below.

Answer to Problem 12CCSR

The option G is correct option.

Explanation of Solution

Given:

  

Concept used:

The dashed line shows the line is not include in the equation.

In inequality the area under line show the solution of the inequality equation.

Putting the value of $x$ and $y$ the equation can be derived.

Calculation:

The boundary line is dashed so inequality is line is not included either its $<\text{or >}$ .

Out of four option F and G is excluded since, line $y=2x$ is drawn dashed form so, both of option is excluded.

Now the equation is either G or H.

Option G is $\text{y<}2\text{x}$ .

Assigning the point that is on the shaded region $\left(1,0\right)$ .

  $\begin{array}{l}y<2x.\\ \Rightarrow 0<2\left(1\right).\\ \Rightarrow 0<2.\end{array}$

So, the option G is true since, $0\text{is less than }2.$

Option H is $\text{y>}2\text{x}$ .

Assigning the point that is on the shaded region $\left(1,0\right)$ .

  $\begin{array}{l}y>2x.\\ \Rightarrow 0>2\left(1\right).\\ \Rightarrow 0>2.\end{array}$

Here the option H is wrong since, $0\text{ cannot be greater than }2.$

Hence, option G is correct option.