The problem asks whether the region where $y > 3x + 4$ should be shaded above or below the line $y = 3x + 4$. We are given that the point $(3, -4)$ lies below the line $y=3x+4$.

1. Problem Description

The problem asks whether the region where $y > 3x + 4$ should be shaded above or below the line $y = 3x + 4$. We are given that the point $(3, -4)$ lies below the line $y=3x+4$.

2. Solution Steps

Since we want to graph the region where $y > 3x + 4$, we need to determine which side of the line to shade. We can use the point $(3, -4)$ as a test point. If $(3, -4)$ satisfies the inequality $y > 3x + 4$, then we would shade the region containing $(3, -4)$. Otherwise, we shade the region on the other side of the line.

Substitute $x = 3$ and $y = -4$ into the inequality $y > 3x + 4$:

$-4 > 3(3) + 4$

$-4 > 9 + 4$

$-4 > 13$

This statement is false. Therefore, the point $(3, -4)$ does not satisfy the inequality $y > 3x + 4$. Since $(3, -4)$ lies below the line, and it does not satisfy the inequality, we should shade the region above the line.

3. Final Answer

Above the line