Question

Which linear inequality is represented by the graph?

Answer 1

Answer:

Correct choice is B.

Step-by-step explanation:

First, determine the equation of the boundary line. This line passes through the points (3,0) and (0,-1). Then its equation is

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

This line is solid on the diagram, then the sign of the inequality should be with the notion "or equal to" (≤ or ≥). Also this line divides the coordinate plane into two regions. The origin belongs to the shaded region, thus, the coordinates (0,0) of the origin must satisfy the inequality. Since

$0\ge \dfrac{1}{3}\cdot 0-1,$

the correct inequality is in option B.

Answer 2

The correct answer is B: y ≥ 1/3x - 1

(0,0) ⇒ within the shaded area

0 ≥ 1/3(0) - 1
0 ≥ 0 - 1
0 ≥ -1
True

(0, -3) ⇒ not within the shaded area

-3 ≥ 1/3(0) -1 
-3 ≥ 0 - 1 
-3 ≥ -1
False