Name: ____________________________________________ Date: ____________ Period: ____
Rates of Change
1. This graph shows the distance a horse traveled toward a barn and the time it took
to get there. Carefully READ the Graph LABELS!!! The barn is at distance = 0.
Which of the following sentences is a
good match for the graph?
50
a. A horse was 9 yards from a
barn, trotted toward it,
reaching it after 45 seconds.
b. A horse was 45 yards from a
barn, trotted toward it,
reaching it after 9 seconds.
c. A horse was 45 yards from a
barn, trotted toward it at a rate
of 9 yards per second.
d. A horse was at the barn and
trotted away from it at a rate of
9 yards per second.
45
Distance (yards)
40
35
30
25
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9 10
Time (seconds)
2. Complete the table that also tells
the story of the graph.
Time (sec)
Distance
(yards)
0
1
2
3
4
5
6
7
8
9
3. Draw AND clearly LABEL a graph for EACH of the three stories in number one that
didn’t explain the given graph.
1
Name: ____________________________________________ Date: ____________ Period: ____
4. You are finished with the horse. Now, create a graph and write your own story for
these two tables.
Time
(seconds)
0
2
4
6
8
10
12
Distance
(meters)
0
6
12
18
24
30
36
Time
(seconds)
0
1
2
3
4
5
6
Distance
(meters)
24
20
16
12
8
4
0
5. A baby was 9 feet from the edge of the porch. (Call the edge of the porch 0 feet.)
He crawled toward the edge for 2 seconds. Then his mother picked him up a few
feet before he reached the edge. Circle the graph below that matches the story.
(0,9)
(0,9)
(2,9)
Dista nce
Dista nce
Dista nce
Dista nce
(0,3)
(2,3)
(2,3)
(2,0)
Time
Time
Time
Time
6. Write a story using the mom and baby scenario for the three graphs from number 5
that you didn’t choose.
2
Name: ____________________________________________ Date: ____________ Period: ____
7. Mother was standing 20 feet from the edge of the porch. She ran toward the baby.
Using information about baby from number 5, sketch a graph for this story. Explain
your graph!
8. Create a graph for each of these stories.
a. A dog was 25 feet away from the doghouse. (Doghouse is at 0 feet.) It
reached the doghouse after 5 seconds.
b. A cat stood still for 3 seconds when she was 15 feet away from the dog. (Dog is
at 0 feet.) Then she ran further away. In five seconds, she was 45 feet away.
3
Name: ____________________________________________ Date: ____________ Period: ____
9. Here is a graph and table that describes a runner’s distance from the finish line in
the last seconds of the race.
Time
(seconds)
0
1
2
3
4
5
6
Distance
(yards)
42
35
28
21
14
7
0
y
(0, 42)
Dista nce
(ya rds)
(6,0)
x
Time (sec onds)
Select the equation below that tells the same story as the table and graph. Choose the
equation by testing every coordinate pair in your equation. Each set of points must be
TRUE for the equation for it to tell the story.
a. y = 7x + 42
b. y = 42 – 6x
c. y = 42 – 7x
d. y = 42x + 6
4
Name: ____________________________________________ Date: ____________ Period: ____
10. Complete the table for this graph.
Time (sec)
(3, 23)
0
1
2
3
Dista nce
Distance
(feet)
5
(0, 5)
Time
Write a story for this graph.
Which equation matches your story, the graph and the table? Check your chosen
equation by testing every coordinate pair in your equation.
a) y = 5 + 6x
b) y = 5x + 23
c) y = 3x + 5
d) y = 5x + 3
Explain your choice.
5