Question

Which linear inequality is represented by the graph?

A.y ≤1/3 x − 1
B.y ≥1/3 x − 1
C.y < 3x − 1
D.y > 3x − 1

Answer 1

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

Answer 2

Correct choice is B.

Explanation:

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

`(x-0)/(3-0)=(y-(-1))/(0-(-1)),\\ \\x=3(y+1),\\ \\y=(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 (1)/(3)\cdot 0-1,`

the correct inequality is in option B.