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

Answer:

Option B.

Step-by-step 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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-3=\dfrac{4-3}{2-0}(x-0)$

$y-3=\dfrac{1}{2}x$

Add 3 on both sides, we get

$y=\dfrac{1}{2}x+3$

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

$y\leq \dfrac{1}{2}x+3$

Therefore, the correct option is B.