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
$y > 2x + 4$
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, confirm which schools are not in Truck A's area ($y > 2x + 4$):

• EZHS: Check coordinates (e.g., $(-8, 6)$): $6 > 2(-8)+4 \to 6 > -12$, so covered by A.
• PMS: Check coordinates (e.g., $(4, 4)$): $4 > 2(4)+4 \to 4 > 12$, false (uncovered).
• The lower-right schools (e.g., $(3,1), (3,-8)$): $1 > 2(3)+4 \to 1>10$; $-8>2(3)+4 \to -8>10$, both false (uncovered).
• The dark shaded schools (NSHS, GMS, MMMS) are already in $y > 2x + 4$, so covered by A.

Step2: Define Truck B's inequality

We need an inequality that covers all uncovered schools (where $y \leq 2x + 4$). A simple, complete coverage is the complement of Truck A's area:
$$y \leq 2x + 4$$
This includes all points on or below the line $y=2x+4$, which covers PMS and the lower-right schools.

Step3: Graphing instructions

1. For Truck A: Draw the dashed line $y=2x+4$ (dashed because the inequality is $>$), then shade the region above the line.
2. For Truck B: Use the same line $y=2x+4$, draw it as a solid line (because the inequality is $\leq$), then shade the region below and on the line.

Answer:

Truck B's route/area is defined by the inequality $\boldsymbol{y \leq 2x + 4}$. When graphing:

• Draw a dashed line for $y=2x+4$ and shade above it for Truck A.
• Draw a solid line for $y=2x+4$ and shade below/on it for Truck B. This ensures all schools are covered.