Question

Which linear inequality is represented by the graph? y ≤ 2x + 4 y ≤ one-halfx + 3 y ≥ One-halfx + 3 y ≥ 2x + 3

Answer 1

y ≤ one-halfx + 3

Explanation:

Answer 2

Option B.

Explanation:

From the given graph it is clear that the related line passes through the points (0,3) and (2,4).

So, the equation of related line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-3=(4-3)/(2-0)(x-0)`

`y-3=(1)/(2)x`

Add 3 on both sides, we get

`y=(1)/(2)x+3`

The related line is a solid line and shaded portion lies below the line. So, the sign of inequality must be ≤.

`y\leq (1)/(2)x+3`

Therefore, the correct option is B.