Question

1. directions

first, select the line a button to graph the line and choose a line style. then, select the solution set button and choose the desired region.
graph the following inequality ( y leq -\frac{2}{3}x + 6 )
(there is a coordinate grid, a line a button with line type: solid dropdown, and a solution set label below the button.)

Explanation:

Step1: Identify boundary line type

Since the inequality is $y \leq -\frac{2}{3}x + 6$ (includes equality), use a solid line.

Step2: Find intercepts of boundary

• y-intercept: Set $x=0$, $y = -\frac{2}{3}(0) + 6 = 6$. Point: $(0, 6)$
• x-intercept: Set $y=0$, $0 = -\frac{2}{3}x + 6$

$\frac{2}{3}x = 6$
$x = 6 \times \frac{3}{2} = 9$. Point: $(9, 0)$

Step3: Determine solution region

Test origin $(0,0)$: $0 \leq -\frac{2}{3}(0) + 6$ → $0 \leq 6$, which is true. Shade the region containing $(0,0)$ (below the line).

Answer:

1. Plot the solid line through points $(0, 6)$ and $(9, 0)$.
2. Shade the region below this solid line.