graph the inequality.\n$3x - y \\leq 6$\nuse the graphing tool to graph the inequality.\nclick to enlarge…

Explanation:

Step1: Rewrite inequality to slope-intercept form

Rearrange $3x - y \leq 6$ to solve for $y$: $$ \begin{align*} -y &\leq -3x + 6\ y &\geq 3x - 6 \end{align*} $$

Step2: Identify boundary line

The boundary line is $y = 3x - 6$, which has a slope of $3$ and y-intercept of $-6$. Since the inequality is $\geq$, the line is solid.

Step3: Determine shaded region

Test the origin $(0,0)$ in $y \geq 3x - 6$: $$0 \geq 3(0) - 6 \implies 0 \geq -6$$ This is true, so shade the region that includes the origin (above the boundary line).

Answer:

1. Draw a solid line for $y = 3x - 6$ (passes through $(0, -6)$ and $(2, 0)$).
2. Shade the area above this solid line.