SAT Question bf5f80c6: Answer, Explanation & Desmos Solution

$y < - 4 x + 4$

Which point ( $x$ , $y$ ) is a solution to the given inequality in the $x y$ -plane?

Difficulty:Medium

( $- 4$ , $0$ )

( $0$ , $5$ )

( $2$ , $1$ )

( $2$ , $- 1$ )

Explanation

Correct answer: A.

Choices A, B, and C are incorrect. None of these points are a solution to the given inequality because each point’s y-coordinate is greater than the value of $- 4 x + 4$ for the point’s x-coordinate.

Desmos solution:

Note: Graph the inequality and plot the four points. The only point that lies in the shaded region is (−4, 0).

Enter in Desmos:

$y < - 4 x + 4$
$(- 4, 0)$
$(0, 5)$
$(2, 1)$
$(2, - 1)$

Reviewed and rewritten by CookSAT

Why the other choices are wrong

Choice B

Choice C

Choice D

Choice D is correct. For a point $(x, y)$ to be a solution to the given inequality in the xy-plane, the value of the point’s y-coordinate must be less than the value of $- 4 x + 4$ , where $x$ is the value of the x-coordinate of the point. This is true of the point $(- 4, 0)$ because $0 < - 4 (- 4) + 4$ , or $0 < 20$ . Therefore, the point $(- 4, 0)$ is a solution to the given inequality.

SAT Question bf5f80c6: Linear Inequalities answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong