Question

graph the following inequality
$y \geq 3x - 1$

Explanation:

Step1: Identify boundary line

First, treat the inequality as an equation: $y = 3x - 1$. This is a linear equation in slope-intercept form $y=mx+b$, where slope $m=3$ and y-intercept $b=-1$.

Step2: Plot the boundary line

Since the inequality is $\geq$ (greater than or equal to), draw a solid line for $y = 3x - 1$. Plot the y-intercept at $(0, -1)$, then use the slope to find another point: move 1 unit right and 3 units up to $(1, 2)$, then connect the points with a solid line.

Step3: Determine shaded region

Choose a test point not on the line, e.g., $(0,0)$. Substitute into the inequality:
$$0 \geq 3(0) - 1$$
$$0 \geq -1$$
This is true, so shade the region that includes the test point (the area above the solid line).

Answer:

1. Draw a solid line for $y = 3x - 1$ (passing through $(0, -1)$ and $(1, 2)$).
2. Shade the region above this solid line.