Question

1. instructions

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 geq -2x + 4 )

Explanation:

Step1: Identify boundary line

The boundary is $y = -2x + 4$, solid (due to $\geq$).

Step2: Find intercepts for the line

• y-intercept: Set $x=0$, $y = -2(0)+4=4$, so point $(0,4)$.
• x-intercept: Set $y=0$, $0=-2x+4 \implies x=2$, so point $(2,0)$.

Step3: Determine solution region

Test point $(0,0)$: $0 \geq -2(0)+4 \implies 0\geq4$, false. So shade the region above the line.

Answer:

1. Draw a solid line through points $(0,4)$ and $(2,0)$.
2. Shade the area that lies above this solid line.