The Winning Goal
NAME_________________________
Kaitlin and Brea are teammates on the field hockey team. Their
team is currently near the end of a game. The score is tied, and
one of the current players is tired. The coach has to determine
who to send in as a substitute, Kaitlin or Brea. She needs the
faster player to help set up what could be the winning goal.
The coach collected data for each player earlier in the game.
Kaitlin’s data are shown in the table, and Brea’s data in the graph.
BREA
100
KAITLIN
y
FIELD POSITION (yd)
3
21
5
35
9
63
0
10
20
30
Field Position (yd)
40 50 60 70
80
90
x
TIME (sec)
0
2
4
6
8
10 12
Time (sec)
14
16
18
20
1. Create an equation in slope-intercept form that could be used to predict Kaitlin’s position at
any time.
2. Create an equation in slope-intercept form that could be used to predict Brea’s position at any
time.
3. Which player should the coach send in? How did the equations help you with the decision?
Explain how you arrived at your answer.
Resources for Teaching Math
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Answer Key – The Winning Goal
Kaitlin and Brea are teammates on the field hockey team. Their
team is currently near the end of a game. The score is tied, and
one of the current players is tired. The coach has to determine
who to send in as a substitute, Kaitlin or Brea. She needs the
faster player to help set up what could be the winning goal.
The coach collected data for each player earlier in the game.
Kaitlin’s data are shown in the table, and Brea’s data in the graph.
BREA
100
KAITLIN
y
FIELD POSITION (yd)
3
21
5
35
9
63
0
10
20
30
Field Position (yd)
40 50 60 70
80
90
x
TIME (sec)
0
2
4
6
8
10 12
Time (sec)
14
16
18
20
1. Create an equation in slope-intercept form that could be used to predict Kaitlin’s position at
any time.
y = 7x
Students could determine the slope by using the table or a graph of the data.
2. Create an equation in slope-intercept form that could be used to predict Brea’s position at any
time.
y = 6 x + 10
Students can identify the points (0,10), (5,40), and (15,100) from the graph.
3. Which player should the coach send in? How did the equations help you with the decision?
Explain how you arrived at your answer.
The coach should put Kaitlin in because she is faster. Students should look at the
coefficient of x in each equation, which represents the speed of the player.
Resources for Teaching Math
© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org