Question

Which ordered pairs make both inequalities true? Select two options.

y < 5x + 2

y > One-halfx + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 2, 0) and (0, 1). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 3) and (0, 2). Everything to the right of the line is shaded.
(–1, 3)

(0, 2)
(1, 2)
(2, –1)
(2, 2)

Answer 1

Answer: The correct ordered pairs that make both inequalities true are (1, 2) and (2, 2).

For the first inequality, y < 5x + 2, the line with a positive slope that goes through (negative 2, 0) and (0, 1) represents the inequality. The points (1, 2) and (2, 2) are both above this line, so they do not satisfy the inequality.

For the second inequality, y > One-halfx + 1, the line with a positive slope that goes through (negative 1, negative 3) and (0, 2) represents the inequality. The points (1, 2) and (2, 2) are both to the right of this line and above it, so they satisfy the inequality.

The other ordered pairs, (–1, 3) and (0, 2), are either below the line for the first inequality or to the left of the line for the second inequality, so they do not satisfy both inequalities.