Question

What inequalities satisfy the region R in the diagram?

Answer 1

Answer:

y ≤ -x - 4

x > -1

y ≥ 4

Step-by-step explanation:

For the sloped line, we can see that the y-intercept is -4 and the x-intercept is -4.

This means at x = 0, y = - 4 and at y = 0, x = -4. We also see that the bottom of the line is shaded and that the line is not broken.

Thus, the inequality is; y ≤ -x - 4

For the vertical line, we can see it has only an x-intercept at x = - 1. We also see that the line is broken which means the equal to symbol is not part of the inequality. Also, the shaded part is to the right. Thus, the inequality is:

x > -1

For the horizontal line, we see that it has only a y-intercept at y = 4. We also see that the line is not broken which means the equal to symbol is part of the inequality. Also, the shaded part is above. Thus, the inequality is:

y ≥ 4

Therefore, the inequalities that satisfy the region R are:

y ≤ -x - 4

x > -1

y ≥ 4