Question

The graph of y ≤ -2x + 4 is shown. Which set contains only points that satisfy the inequality? A) {(0, 0), (1, 2), (3, -3)} B) {(0, 0), (1, 2), (7, -2)} C) {(3, 3), (1, 2), (3, -3)} D) {(0, 0), (2, 1), (3, -3)}

Answer 1

To find out if a set satisfies the inequality, you can either plug in the points into the equation, or you can plug in the points into the graph.

Any point in the shaded area and on the line satisfy the inequality. If the inequality had a sign of < or >, then the point can not be on the line, only in the shaded area.

A.) This is a solution because they are all in the shaded area

B.) This is not a solution because (7,-2) is outside the shaded area

C.) This is not a solution because (3,3) is outside the shaded area

D.) This is not a solution because (2,1) is outside the shaded area

Answer 2

A) {(0, 0), (1, 2), (3, -3)}

Explanation:

Check by inserting values into the inequality.

y ≤ -2x + 4

Set A

(0,0): 0≤ 4 TRUE

(1,2): 2 ≤ -2×1 + 4

2 ≤ -2 + 4

2 ≤ 2 TRUE

(3,-3): -3 ≤ -2×3+4

-3 ≤ -6 + 4

-3 ≤ -2 TRUE

=====

Set B

(7, -2): -2 ≤ -2×7 + 4

-2 ≤ -14 + 4

-2 ≤ -10 FALSE

=====

Set C

(3,3): 3 ≤ -2×3 + 4

3 ≤ -6 + 4

3 ≤ -2 FALSE

=====

Set D

(2,1): 1 ≤ -2×2 + 4

1 ≤ -4 +4

1 ≤ 0 FALSE

Set A is the one that contains only points that satisfy the inequality.