Question

3 Look at the three graphs below.

Graph A
y
Graph
Graph B
8
у

7
8
8
7
7
6
Distance (ft)
5
Distance (ft)
Distance (ft)
4
2
3
2
1
2
0
1
X
0
0 1 2 3 4 5 6 7 8
Time (s)
0
0 1 2 3 4 5 6 7 8
Time (s)
0 1 2 3 4 5 6 7 8
Time (s)
True
False
True
False
Based on the graphs, choose True or False for each statement.
a. Graph B shows a proportional relationship
between distance and time.
b. In Graph A, the constant of proportionality
between distance and time is
C. Graph C shows an object that speeds up over time.
d. The unit rate in Graph Bis 2 feet per second.
e. An object represented by Graph A is moving faster
than an object represented by Graph B.
True
DOU
False
True
False
True
False

Answer 1

Graph B does not show a proportional relationship between distance and time, the constant of proportionality in Graph A is not C, Graph C does not show an object that speeds up over time, the unit rate in Graph B is 2 feet per second, and an object represented by Graph A is not moving faster than an object represented by Graph B.

Step-by-step explanation:

a. False. Graph B does not show a proportional relationship between distance and time. In a proportional relationship, the graph would be a straight line passing through the origin (0,0). Graph B shows a curved line, indicating non-proportional relationship.

b. False. In Graph A, the constant of proportionality between distance and time is not C. The constant of proportionality can be determined by finding the slope of the graph, which is the ratio of change in distance to change in time.

c. False. Graph C does not show an object that speeds up over time. A graph showing an object speeding up would have an increasing slope.

d. True. The unit rate in Graph B is 2 feet per second. This can be determined by finding the slope of the graph, which represents the rate of change of distance with respect to time.

e. False. An object represented by Graph A is not moving faster than an object represented by Graph B. The speed of an object cannot be determined solely by looking at the position vs. time graph.

Answer 2

Step-by-step explanation:

a. True

any linear function is a proportional relationship.

b. True

after 3 seconds it moved 4 ft. so 4/3.

c. True

distance grows at a higher rate than time.

speed is distance/time. so, yes, the speed increases.

d. false

the object moves 1 ft for every 1 second. not 2 ft per second.

e. True

we must not get confused by the absolute numbers, because graph B starts already at an offset of 1ft.

but from there it changes only with a rate of 1 ft per second.

while A changes 4 ft per 3 seconds 1.3333... ft per second, which is bigger than 1 ft per second, and therefore the object A is faster.