Question

Which linear inequality represents the solution set graphed?

Answer 1

Answer:

Correct option is C

Step-by-step explanation:

First, find the equation of the boundary line. This line passes through the points (0,-3) and (-2,1). Then it has equation

$\dfrac{x-0}{-2-0}=\dfrac{y+3}{1+3},\\ \\4x=-2(y+3),\\ \\y=-2x-3.$

In the attached diagram this boundary line is solid, then the sign of the inequality should be with "or equal to" notion (≤ or ≥). Thus, options A and B are false.

The line divides the coordinate plane into two parts and you have to determine which part to choose. The origin does not lie in the shaded region, then its coordinates cannot satisfy the inequality. Check options C and D.

$0\le -2\cdot 0-3\ (0\le -3)$ - origin does not satisfy (option C is correct);

$0\ge -2\cdot 0-3\ (0\ge -3)$ - origin satisfies (option D is false).