The problem asks us to graph the solution to the following system of inequalities: $y \ge 3x - 2$ $y \le \frac{3}{4}x$

1. Problem Description

The problem asks us to graph the solution to the following system of inequalities:

$y \ge 3x - 2$

$y \le \frac{3}{4}x$

2. Solution Steps

To graph the system of inequalities, we need to graph each inequality separately and then find the region where their solutions overlap.

First, let's consider the inequality $y \ge 3x - 2$. To graph the line $y = 3x - 2$, we can find two points on the line.

If $x = 0$, then $y = 3(0) - 2 = -2$. So, the point $(0, -2)$ is on the line.

If $x = 1$, then $y = 3(1) - 2 = 1$. So, the point $(1, 1)$ is on the line.

Since the inequality is $y \ge 3x - 2$, we shade the region above the line $y = 3x - 2$. The line itself should be solid because the inequality includes "equal to".

Now, let's consider the inequality $y \le \frac{3}{4}x$. To graph the line $y = \frac{3}{4}x$, we can find two points on the line.

If $x = 0$, then $y = \frac{3}{4}(0) = 0$. So, the point $(0, 0)$ is on the line.

If $x = 4$, then $y = \frac{3}{4}(4) = 3$. So, the point $(4, 3)$ is on the line.

Since the inequality is $y \le \frac{3}{4}x$, we shade the region below the line $y = \frac{3}{4}x$. The line itself should be solid because the inequality includes "equal to".

The solution to the system of inequalities is the region where the shaded regions of both inequalities overlap.

3. Final Answer

The solution is the region where the inequality $y \ge 3x-2$ (the region above the line $y = 3x-2$) overlaps with the inequality $y \le \frac{3}{4}x$ (the region below the line $y = \frac{3}{4}x$). Both lines are solid.