Answer: The graph corresponds to the inequality y > 3x + 2
Step-by-step explanation:
A linear inequality is similar to a linear equation, but it consists of inequality symbols (<, >, ≤, ≥) rather than the equal sign (=).
In the question, the linear inequality is depicted through a graph.
The line in the graph intersects the point (-3,-7).
Now, let’s evaluate which option meets the conditions of this point.
1) y < 3x + 2 implies the line should be y = 3x + 2.
⇒ -7 = 3(-3) + 2.
⇒ -7 = -9 + 2 ⇒ -7 = -7, which holds true.
2) y > 3x + 2, which is analogous to the first.
3) y < x + 2 means the line should be y = x + 2.
⇒ -7 = -3 + 2.
⇒ -7 = -1, which is false.
4) y > x + 2 parallels the third scenario.
Thus, options 3) and 4) cannot represent the required linear inequality.
From options 1) and 2), option 2) is the correct linear inequality since the graph indicates shading above the line, suggesting y (>) must be greater. [Conversely, for y (<) to be lower, the shading would be below the line.]
Consequently, the correct linear inequality presented by the graph is 2) y > 3x + 2.
