Question

5
graph the following inequality
$y \geq 3x - 1$

Explanation:

Step1: Identify boundary line type

Since the inequality is $\geq$ (includes equality), use a solid line for $y=3x-1$.

Step2: Plot the boundary line

The line $y=3x-1$ has a slope $m=3$ and y-intercept $b=-1$.

• Plot the y-intercept: $(0, -1)$
• Use slope to find a second point: from $(0,-1)$, move 1 right, 3 up to $(1, 2)$
• Draw a solid line through these points.

Step3: Determine shaded region

Test a point not on the line, e.g., $(0,0)$:
Substitute into $y\geq3x-1$:
$0\geq3(0)-1$
$0\geq-1$, which is true.
Shade the region above and including the solid line (where the test point lies).

Answer:

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