Chapter 6, Problem 10PFA

To determine

To find: The inequality that describe the graph.

Answer to Problem 10PFA

The inequality that describe the graph is $2x+y\ge 4$ .

Explanation of Solution

Given information:

The graph of the inequality is shown in Figure-1.

Formula used:

We obtain equation of straight line on the graph. If $\left(a,0\right)$ and $\left(0,b\right)$ are x -intercept and y -intercept of the line then its equation is $\frac{x}{a}+\frac{y}{b}=1$

Calculations:

The x - intercept and y-intercepts of the line that describe the inequality are $\left(4,0\right)$ and $\left(0,2\right)$ .

Hence, equation of line is $\frac{x}{4}+\frac{y}{2}=1$ or $2x+y=4$ .

Since, the inequality describe the region away from the origin, hence the inequality that describe the graph is $2x+y\ge 4$ .

(Note: If inequality would describe region including origin then inequality would have been $2x+y\le 4$ )

Conclusion:

The inequality that describe the graph is $2x+y\ge 4$ .