1 Answer

Talles · Answer 1 · 2018-07-10T09:39:13+0000

Answer:

The linear inequality that is represented by the graph is:

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

From the graph of the given function we see that the graph is a solid line passing through (0,3) and (-6,0) and the shading is towards the origin.

Hence, we will check each of the given options.

A)

$y\leq 2x+4$

We see that the line of this inequality is a line passing through (0,4) and (-2,0) and shading towards the origin.

Hence, option: A is incorrect.

C)

$y\geq (1)/(2)x+3$

The graph of this inequality is a solid line passing through (0,3) and (-6,0) and the shading is away from the origin.

Hence, option: C is incorrect.

D)

$y\geq 2x+3$

The graph of this inequality is a solid line passing through the point (0,3) and (-3/2,0) and shading away from the origin.

Hence, option: D is incorrect.

B)

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

When we plot the graph of this inequality we see that it matches the given graph.

Hence, option: B is the correct answer.