Question

graph the linear inequality. $y \geq 3x$
use the graphing tool to graph the inequality.
click to enlarge graph

Explanation:

Step1: Graph the boundary line

First, identify the boundary line $y=3x$. This is a straight line with slope $3$ and y-intercept $0$. Since the inequality is $\geq$, we use a solid line (not dashed) to include points on the line.

Step2: Test a point for shading

Choose a test point not on the line, e.g., $(0,1)$. Substitute into the inequality: $1 \geq 3(0) \implies 1 \geq 0$, which is true. So we shade the region that contains $(0,1)$ (the area above the line $y=3x$).

Answer:

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