Question

Which set of points contains the solutions to the inequality y ≥ 1⁄4x + 5?

A. {(–3,–17), (4,11), (7,19)}
B. {(4,6), (8,8), (–3,6)}
C. {(3,4), (2,3), (8,27)}
D. {(–2,–1), (4,–7), (5,1)}

Answer 1

B. {(4,6), (8,8), (–3,6)}

Explanation:

You can graph the equation and plot the points, or you can try the points algebraically. For the latter, it is convenient to rearrange the inequality a bit.

y ≥ 1/4x + 5 . . . . . given

4y ≥ x + 20 . . . . . multiply by 4

You can use this form, or you can subtract x to get ...

4y -x ≥ 20

Trying the offered points, we want 4y-x to be at least 20. We get ...

A: 4(-17) -(-3) = -65 . . . . less than 20

B: 4(6)-4 = 20 . . . a solution

4(8) -8 = 24 . . . a solution

4(6)-(-3) = 27 . . . a solution . . . . set B contains solutions to the inequality

C: 4(4)+3 = 19 . . . . less than 20

D: 4(-1)-(-2) = -2 . . . . less than 20