graph this inequality: y ≤ -2x + 4 plot points on the boundary line. select the line to switch between solid…

Explanation:

Step1: Identify the boundary - line equation

The boundary - line for the inequality $y\leq - 2x + 4$ is the equation $y=-2x + 4$.

Step2: Find two points on the boundary - line

When $x = 0$, $y=-2(0)+4=4$. So one point is $(0,4)$. When $y = 0$, $0=-2x + 4$, then $2x=4$, $x = 2$. So another point is $(2,0)$.

Step3: Determine the type of the boundary - line

Since the inequality is $y\leq - 2x + 4$ (the symbol is $\leq$), the boundary - line is solid.

Step4: Test a point to determine the shaded region

Test the point $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequality: $0\leq-2(0)+4$, which is $0\leq4$ (a true statement). So the region that contains the origin $(0,0)$ is shaded.

Answer:

1. Plot the points $(0,4)$ and $(2,0)$ on the coordinate plane.
2. Draw a solid line passing through these two points.
3. Shade the region below the solid line (the region that contains the origin $(0,0)$).