SAT Linear inequalities in one or two variables Practice Question 13 (Medium)

Question bank / Linear inequalities in one or two variables

Math · AlgebraMedium

In the $xy$ -plane, the point $(-1, -5)$ is in the solution set of which of the following inequalities, while the point $(0, 0)$ is not?

$y > 3x - 1$

$y > -3x - 1$

$y < -3x + 1$

$y < 3x - 1$

Show answer and explanation

Answer: D

For choice D, $(-1, -5)$ gives $-5 < 3(-1) - 1 = -4$ , which is true, and $(0, 0)$ gives $0 < -1$ , which is false. So B works. Each other choice includes $(0, 0)$ : $0 > -1$ , $0 < 1$ , and $0 > -1$ are all true.

Choice C contains $(-1, -5)$ , since $-5 < 4$ , but it also contains $(0, 0)$ , so it fails the second condition.

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