Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < x + 2
y > x + 2

The graph is represented by the inequality y>3x+2

Step-by-step explanation:

Linear inequality is like linear equation just we have inequality signs (<,>,≤,≥) instead of equal sign(=).

In the given question we have the linear inequality represented by graph

We can see the line in the graph passing through the point (-3,-7)

Let's check which option satisfy the point

1) y<3x+2 for this the line should be y=3x+2

⇒ -7=3(-3)+2

⇒-7= -9+2⇒-7=-7,which is true.

2) y>3x+2 which similar as first.

3) y<x+2 for this the line should be y=x+2

⇒ -7= -3+2

⇒-7=-1 which is not true.

4) y > x + 2 is similar to third.

Option 3) and 4) cannot be the required linear inequality.

Now from 1) and 2) , 2) should be the required linear inequality as the graph is shaded above the line and that must be for y (>) greater than inequality. [ for y (<) less than inequality the graph must be shaded below the line]

Therefore, 2)  y > 3x + 2 is the required linear inequality which is represented by the graph.