Question

1. graph the linear inequality below.

$y \geq -x + 4$

Explanation:

Step1: Identify boundary line

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

Step2: Find intercepts of boundary

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

Step3: Test a point for shading

Use $(0,0)$: $0 \geq -0 +4 \implies 0 \geq 4$, which is false.
Shade the region not containing $(0,0)$ (above the line).

Step4: Plot and shade

Draw solid line through $(0,4)$ and $(4,0)$, shade the area above the line.

Answer:

1. Draw a solid straight line connecting the points $(0, 4)$ and $(4, 0)$ on the provided coordinate plane.
2. Shade the entire region that lies above this solid line.