Download 8M.3.2.1sketchinterpretmodels

Name _______________________________________ Date _______________
Objective: 8M.3.2.1
Sketch and interpret a graph that models a given context, describe a context that
is modeled by a given graph.
____________________________________________________
1. Which path below would describe a race car that started slowly at first and
gradually increased its speed?
A. Y
B. X
C. W
D. Z
2. You have 200 pounds of clay to use for making bowls and vases. You need
4 pounds of clay for each bowl and 2.5 pounds of clay for each vase. Which
inequality represents the possible numbers of bowls and vases you can
make? Graph the correct inequality.
A. 4b + 2.5v < 200
B. 4b + 2.5v 200
C. 4v + 2.5b 200
D. 4b + 2.5v > 200
E. 4b + 2.5v 200
3. Billy ran up a hill. Billy's position changed horizontally 2 feet for every 1/2 foot of
vertical change as he ran up the hill. Which graph below shows Billy's
movement?
A. X
B. Y
C. W
D. Z
4. Marissa noticed that the price of chocolate milk at her school has increased
at a constant rate since she was in first grade. Which of the following graphs
accurately represents this situation?
A. W
B. X
C. Y
D. Z
5. You have a $100 gift card to a store that rents movies and video games.
The rental fee for a movie is $4.00 and the rental fee for a video game is
$5.00. Which inequality represents the possible numbers of movies and
video games you can rent? Using intercepts, graph the correct inequality.
A. 4m + 5v < 100
B. 4m + 5v 100
C. 5m + 4v 100
D. 4m + 5v > 100
E. 4m + 2.5v 100
8M.3.2.1 Key
1.
2.
3.
4.
5.
D
E
C
A
B
Explanations
1. Graph X shows a car that started off slow and then gradually
increased its speed. As the car's acceleration increased, the slope of
the line increased steeply, which created the curved line.
Graph W shows a car that started fast and then slowed down.
Graph Y shows a car that was stopped and then accelerated quickly.
Graph Z shows a car that traveled at a constant speed.
2. The amount of clay that can be used is “less than or equal to” 200, the sign
used must be >
Let “b” represent the amount of clay needed for a bowl, and “v” the
amount of clay needed for a base. The correct inequality is:
4b + 2.5v 200
Use the intercepts to determine two points on the graph.
When b = 0, v = 80. When v = 0, b = 50. Connect the two points to create the
graph, and shade in all the area in the quadrant beneath the line.
3. For every 2 feet that Billy runs horizontally (shown on x-axis), he
runs 1/2 foot vertically (shown on y-axis). So, after running 4 feet
horizontally, he would have run 1 foot vertically, and so on.
Notice that graph W contains the point (4,1). This is a clue that
graph W is correct.
4.
In graph X, the price increases, but the grade decreases. Therefore, X
is not the correct graph.
In graph Y, the price increases, but does not increase at a constant
rate. Therefore, Y is not the correct graph.
In graph Z, the price increases, but does not increase at a constant
rate. Therefore, Z is not the correct graph.
In graph W, the price increases at a constant rate as her grade
increases. Therefore, W is the correct graph.
5. The amount of money that can be used is “less than or equal to” $100, the sign used
must be > . Let “m” represent the rental cost of a movie, and “v” the
rental cost of a video game. The correct inequality is:
4m + 5v $100
Use the intercepts to determine two points on the graph.
When m = 0, v = 20. When v = 0, m = 25. Connect the two points to create the
graph, and shade in all the area in the quadrant beneath the line.