Chapter 6.5, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

For the graph of the inequality $x-2y\ge 4,$ what is a value of $x$ for a point that is on the boundary line and the axes?

F. $4$

G. $-2$

H. $2$

I. $-4$

To determine

The value of x for a point that is on the boundary line of inequality $x-2y\ge 4$ and the axes.

Explanation of Solution

Given information:

The point $\left(x,y\right)$ lies on the boundary of inequality $x-2y\ge 4$ and axes, where x is

F. 4

G. -2

H. 2

I. - 4

Method used:

The graph is sketched using graphing calculator.

Graph:

The graph of inequality $x-2y\ge 4$ is shown in Figure-1 here.

  

The shaded region is the graph of inequality $x-2y\ge 4$ .

We observe that points $\left(4,0\right)$ and $\left(0,-2\right)$ lie on the boundary of inequality $x-2y\ge 4$ and the axes.

Thus, the points for which $x=0$ and $x=4$ lie on the boundary of inequality $x-2y\ge 4$ and the axes.

Hence, the option F is correct.

Conclusion:

The option F is correct.