Question

our trucks made another great effort yesterday but there was still some area uncovered. we are getting desperate and we need your help.
snow truck a
covers the area
$y > 2x + 4$
$y=2x+4$
snow truck b
travels the path
yesterday we got majority of our schools covered but there were still some areas we needed to get.
by using what you know about graphing equations, we need you to come up with a route for truck b that makes sure we get all schools covered.
graph and shade truck as area and your new area on the graph.

Explanation:

Step1: Identify uncovered schools

First, observe the graph: the shaded area is $y > 2x + 4$, which covers NSHS, GMS, MHMS. The uncovered schools are ESHS, PHS, and the two lower-right points, all in the region $y \leq 2x + 4$.

Step2: Define Truck B's area

To cover all remaining schools, we need a linear inequality whose region includes all points not in $y > 2x + 4$. The complementary region is $\boldsymbol{y \leq 2x + 4}$. This uses a solid line for $y=2x+4$ (to include the boundary) and shades below/on the line.

Step3: Verify coverage

Check that ESHS, PHS, and the lower-right points satisfy $y \leq 2x + 4$:

• For ESHS (e.g., $(-6, 4)$): $4 \leq 2(-6)+4

ightarrow 4 \leq -8$, which is false. Wait, correct the inequality to cover upper-left and right points: the correct region to cover all uncovered schools is $\boldsymbol{y \leq 2x + 4}$ does not work for ESHS, so we need a different inequality. Let's use $\boldsymbol{y < 2x + 10}$ (adjusted to include ESHS: $4 < 2(-6)+10
ightarrow 4 < -2$ no. Correct approach: find a line that separates covered and uncovered. The covered area is $y>2x+4$, so uncovered is all points where $y \leq 2x + 4$ is not true? No, ESHS is above $y=2x+4$? Wait $y=2x+4$ at $x=-6$ is $y=2(-6)+4=-8$, ESHS is at $y=4$, which is $4 > -8$, so ESHS is in $y>2x+4$ but not shaded. Oh, the shaded area is below? No, the dark shaded area is below $y=2x+4$. So Truck A's area is actually $y < 2x + 4$ (mislabeled). Then uncovered is $y \geq 2x + 4$. So Truck B's area is $\boldsymbol{y \geq 2x + 4}$.

Step4: Confirm all schools covered

• Truck A: $y < 2x + 4$ (shaded dark, covers NSHS, GMS, MHMS)
• Truck B: $y \geq 2x + 4$ (shaded light, covers ESHS, PHS, lower-right points)

All schools are now covered.

Answer:

Truck B's route/area is defined by the inequality $\boldsymbol{y \geq 2x + 4}$. To complete the graph:

1. Draw the solid line $y=2x+4$ (since the inequality includes equality).
2. Shade the region above and on this line. This will cover all the previously uncovered schools (ESHS, PHS, and the two points in the lower-right quadrant), ensuring all schools are covered when combined with Truck A's area $y > 2x + 4$ (or corrected $y < 2x + 4$ as per the shaded graph).