Question

Which answer choice correctly states the type of boundary line, the shading, and a point in the solution set of the inequality -14 + 2y < -x?

A. Solid boundary line; shaded above; (8, 8)
B. Dashed boundary line; shaded above; (8, 8)
C. Solid boundary line; shaded below; (0, 0)
D. Dashed boundary line; shaded below; (0, 0)

Answer 1

The correct answer choice is D. Dashed boundary line; shaded below; (0, 0).

Step-by-step explanation:

The inequality -14 + 2y < -x represents a line in a coordinate plane. To determine the type of boundary line, we need to consider the inequality symbol. Since the symbol is '<', the boundary line is dashed. Next, to determine the shading, we need to test a point in the solution set of the inequality. Let's use the point (8, 8). Substitute this point into the inequality: -14 + 2(8) < -(8). Simplifying, we get -14 + 16 < -8. This simplifies to 2 < -8, which is false. Therefore, the point (8, 8) is not in the solution set. Based on this, the correct answer choice is D. Dashed boundary line; shaded below; (0, 0).