1
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
TASK 2.13.5: SCAVENGER HUNT — STUDENT VERSION
Solutions
Note: In the interest of time and space, solutions for Clues 1–3 are only provided with
Round 1. Answers for Rounds 2–4 are similar.
Suppose you are a participant of a scavenger hunt in a cornfield in Iowa. You are given the
coordinates to your starting point S = (12, 60), to your best friend’s location F = (-8, 20), and to
your home base point H = (-30, -24).
Round 1: To complete the first leg of the hunt, you must find 8 items. Here are your clues.
Clue #1: Your first two items,  and , are located due east or due west of point H and point
F, respectively. The slope of the line through S and  is twice that of the line formed by S and
H.  is also located on the line through S and .
1. Where are  and  located?
Students may think about this problem using finite differences.
( 12, 60)
-42 
 -84
So the slope is -84/-42 = 2.
( -30, -24)
( 12, 60)
-21 
 -84
( ? , -24)
Here the slope needs to be 4, so -84
divided by the differences in the x’s
must be 4. Thus the differences in the
x’s must be -21. This means that
? - 12 = -21 so ? = -9.
Thus  is located at point (-9, -24). The y-intercept of the line between S and  is 12. Since
 is located due east or due west of F, it must look like (?, 20). It is also on the line between S
and , so by plugging this point into the line’s equation, we see that  is located at (2, 20).
2. What is the change in the x-values of S and H? S and F? 42; 20
3. What is the change in the x-values of S and ? S and ? 21; 10
4. What do you notice about the change in x-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in x-values of S and  compared
to the change in x-values of S and F? The change in the x-values S and H is twice the
difference of the x-values of S and . Similarly the change in the x-values S and F is twice
the difference of the x-values of S and .
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
5. What do you notice about the change in the y-values of S and  and the change in the
y-values of S and B? The difference in the y-values is the same with both sets of points.
6. Find the y-intercept of the line through S and H and the y-intercept of the line through S and
. (0, 36); (0, 12)
Clue #2: Your next two items,  and , are located due east or due west of H and F,
respectively. The slope of the line through S and  is one-third of the slope of the line formed
by S and H.  is also located on the line through S and .
1. Where are  and  located?
Students may think about this problem using finite differences.
( 12, 60)
-42 
 -84
So the slope is -84/-42 = 2.
 -84
Here the slope needs to be 6, so -84
divided by the differences in the x’s
must be 6. Thus the differences in the
x’s must be -14. This means that
? - 12 = -14 so ? = -2.
( -30, -24)
( 12, 60)
-14 
( ? , -24)
Thus is located at point (-2, -24). The y-intercept is located at -12. By a similar process
to the one above,  is located at (16/3, 20).
2. What is the change in the x-values of S and H? S and F? 42; 20
3. What is the change in the x-values of S and ? S and ? 14; 20/3
4. What do you notice about the change in x-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in x-values of S and  compared
to the change in x-values of S and F? Notice that the change in the x-values of S and H is
three times that of the change in x-values of S and . Similarly, the change in x-values of
S and F is three times that of S and .
5. What do you notice about the change in the y-values of S and  and the change in the
y-values of S and B? The difference in the y-values is the same with both sets of points.
6. Find the y-intercept of the line through S and H and of the line through and S.
(0, 36), (0, -12)
.
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Clue #3: Your next items,  and , are located due east or due west of H and F, respectively.
The slope of the line through S and  is four times that of the line formed by S and H.  is
located on the line through S and .
1. Where are  and  located?
Students may think about this problem using finite differences.
( 12, 60)
-42 
 -84
( -30, -24)
( 12, 60)
-21/2 
 -84
( ? , -24)
So the slope is -84/-42 = 2.
Here the slope needs to be 8, so -84
divided by the differences in the x’s
must be 8. Thus the differences in the
x’s must be -42/4 = -21/2. This means
that ? - 12 = -21/2 so ? = 3/2.
Thus  is located at point (3/2, -24). The y-intercept is located at -36.
2. What is the change in the x-values of S and H? S and F?
42; 20
3. What is the change in the x-values of S and ? S and ?
21/2; 5
4. What do you notice about the change in x-values of S and  compared to the change in
x-values of S and H? What do you notice about the change in x-values of S and  compared
to the change in x-values of S and F? Notice that the change in the x-values of S and H is
four times that of S and . Similarly, the change in the x-values of S and F is four times
that of S and .
5. What do you notice about the change in the y-values of S and  and the change in the yvalues of S and B? The difference in the y-values is the same with both sets of points.
6. Find the y-intercept of the line through S and H and the y-intercept of the line through  and
S. (0, 36); (0, -36)
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
1. Using the graph and the information that you have gathered in your search for the first six
items, make a conjecture about the location of your last two items,  and , that are
located due east or due west of H and F, respectively, given that the slope of the line through
S and  is seven times that of the line formed by S and H and that  is on the line through
S and . Explain your reasoning. The lines are becoming more vertical. Noticing the
patterns from the previous three exercises, students should come up with the conjecture that
the difference in the x-values of  and S should be one-seventh of the difference between
the x-values of S and H. That is, the difference in the x-values should be 1/7*(-42)=-6.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
2. Show that your conjecture is correct. To see this, we use the same method as before.
( 12, 60)
-42 
 -84
So the slope is -84/-42 = 2.
 -84
Here the slope needs to be 14, so -84
divided by the differences in the x’s must
be 14. Thus the differences in the x’s
must be -6. This means that ? - 12 = -6
so ? = 6.
( -30, -24)
( 12, 60)
-6 
( ? , -24)
Thus the item is located at point (6, -24).
3. Using the information obtained from the first three clues complete the following table. Note
let m=slope of the line through S and H. What is the relation of n to the change in the slope?
(x1,y1) (x2,y2)
B=y-intercept
(0, 36)
Let K=Change in yintercepts
Not applicable
B=y1-n*m*x1
What’s n?
Not applicable
S = (12, 60) H=(-30, -24)
S = (12, 60) =( -9, -24)
(0, 12)
-24
12=60-(2)(2)(12)
S = (12, 60) =( -2, -24 ) (0, -12)
-24
-12=60-(3)(2)(12)
S = (12, 60) =( 3/2, -24) (0, -36)
-24
-36=60-(4)(2)(12)
S = (12, 60) =( 6, -24 )
Not applicable
-60=60-(7)(2)(12)
(0, -108)
Note that in the chart, the n is the same as the multiplier of the slope.
Concluding question: If we continued the process above, would we ever get a line that was
vertical? Why or why not?
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
-60
-50
-40
-30
H
-20
-10
F
1
65
60
55
50
45
40
35
30
25
20
15
10
5
-5
-10
-15
-20
-25
3
-30
2
5
4
10
S
3
6 8
7
20
30
40
50
60
70
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Round 2: You must find 4 items to complete this round.
Clue #1: Your first item is located due east or due west of your base point. The slope of the line
through the starting point and the point of the item’s location is half that of the line formed by
the starting point and your base point. Where is the item located? Notice that the change in the
x-values of the starting point and the base point is –42. Explain the relationship between the
change in the x-values of the starting point and item #1’s location and the change in the x-values
of the starting point and the base point. Also what do you notice about the change in the yvalues of the starting point and item #1’s location and the change in the y-values of the starting
point and the base point?
Clue #2: Your second item is located due east or due west of your base point. The slope of the
line through the starting point and the point of the item’s location is one-third of that of the line
formed by the starting point and your base point. Where is the item located? Explain the
relationship between the change in the x-values of the starting point and item #2’s location and
the change in the x-values of the starting point and the base point. Also what do you notice
about the change in the y-values of the starting point and item #1’s location and the change in the
y-values of the starting point and the base point?
Clue #3: Your third item is located due east or due west of your base point. The slope of the
line through the starting point and the point of the item’s location is one-fourth that of the line
formed by the starting point and your base point. Where is the item located? Explain the
relationship between the change in the x-values of the starting point and item #3’s location and
the change in the x-values of the starting point and the base point. Also what do you notice
about the change in the y-values of the starting point and item #1’s location and the change in the
y-values of the starting point and the base point?
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
What do you notice about the slope of the lines? Using the graph and the information that you
have gathered in your search for items 1, 2, and 3, make a conjecture about the distance in the xvalues of the location of an item that is located due east or due west of your base point and the
starting point given that the slope of the line through the starting point and the point of the item’s
location is one-seventh of the slope of the line formed by the starting point and your base point.
Show that your conjecture is correct.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
140
120
100
80
60
Start
40
20
-150
-100
-50
50
100
150
-20
#3
#2
#1
Base
-40
-60
-80
-100
-120
-140
Concluding question: If we continued the process above, would we ever get a line that was
horizontal? Why or why not?
Round 3: You must collect 4 items to complete this round.
Clue #1: Your first item is located due north or due south of your base point. The slope of the
line through the starting point and the point of the item’s location is twice that of the line formed
by the starting point and your base point. Where is the item located? Notice that the change in
the y-values of the starting point and the base point is –84. Explain the relationship between the
change in the y-values of the starting point and item #1’s location and the change in the y-values
of the starting point and the base point. Also what do you notice about the change in the
y-values of the starting point and item #1’s location and the change in the x-values of the starting
point and the base point?
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Clue #2: Your second item is located due north or due south of your base point. The slope of
the line through the starting point and the point of the item’s location is three times that of the
line formed by the starting point and your base point. Where is the item located? Explain the
relationship between the change in the y-values of the starting point and item #2’s location and
the change in the y-values of the starting point and the base point. Also what do you notice about
the change in the y-values of the starting point and item #2’s location and the change in the xvalues of the starting point and the base point?
Clue #3: Your third item is located due north or due south of your base point. The slope of the
line through the starting point and the point of the item’s location is four times that of the line
formed by the starting point and your base point. Where is the item located? Explain the
relationship between the change in the y-values of the starting point and item #3’s location and
the change in the y-values of the starting point and the base point. Also what do you notice about
the change in the y-values of the starting point and item #3’s location and the change in the xvalues of the starting point and the base point?
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
What do you notice about the slope of the lines? Using the graph and the information that you
have gathered in your search for items 1, 2, and 3, make a conjecture about the differences in the
y-values of the location of an item that is located due north or due south of your base point and
the starting point given that the slope of the line through the starting point and the point of the
item’s location is seven times the slope of the line formed by the starting point and your base
point. Show that your conjecture is correct.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
350
300
250
200
150
100
50
-400
-300
-200
-100
Start
100
Base
200
300
400
-50
#1
-100
-150
#2
-200
-250
#3
-300
-350
Concluding question: Will the line ever be vertical if we continue changing the slope as we have
in the previous exercise? Why or why not? Is this similar to either of the exercises in round 1 or
round 2? Explain.
Round 4: To complete this round, your will need to locate 4 items.
Clue #1: Your first item is located due north or due south of your base point. The slope of the
line through the starting point and the point of the item’s location is half that of the line formed
by the starting point and your base point. Where is the item located? Notice that the change in
the y-values of the starting point and the base point is –84. Explain the relationship between the
change in the y-values of the starting point and item #1’s location and the change in the y-values
of the starting point and the base point. Also what do you notice about the change in the yvalues of the starting point and item #1’s location and the change in the x-values of the starting
point and the base point?
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Clue #2: Your first item is located due north or due south of your base point. The slope of the
line through the starting point and the point of the item’s location is one-third of that of the line
formed by the starting point and your base point. Where is the item located? Explain the
relationship between the change in the y-values of the starting point and item #2’s location and
the change in the y-values of the starting point and the base point. Also what do you notice
about the change in the y-values of the starting point and item #2’s location and the change in the
x-values of the starting point and the base point?
Clue #3: Your first item is located due north or due south of your base point. The slope of the
line through the starting point and the point of the item’s location is one-fourth that of the line
formed by the starting point and your base point. Where is the item located? Explain the
relationship between the change in the y-values of the starting point and item #3’s location and
the change in the y-values of the starting point and the base point. Also what do you notice
about the change in the y-values of the starting point and item #3’s location and the change in the
x-values of the starting point and the base point?
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
What do you notice about the slope of the lines? Using the graph and the information that you
have gathered in your search for items 1, 2, and 3, make a conjecture about the location of an
item that is located due north or due south of your base point given that the slope of the line
through the starting point and the point of the item’s location is one-seventh of the slope of the
line formed by the starting point and your base point. Show that your conjecture is correct.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
80
70
60
Start
50
#3
40
#2
30
20
#1
10
-100
-80
-60
-40
-20
20
40
60
80
100
-10
-20
Base
-30
-40
-50
-60
-70
-80
Concluding question: Will the line ever be horizontal if we continue changing the slope as we
have in the previous exercise? Why or why not? Is this similar to either of the exercises in
round 1 or round 2? Explain.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
TASK 2.13.5: SCAVENGER HUNT — STUDENT VERSION
Scavenger Hunt (Alg. I Student Version)
Objective: After completing this activity, students will have a better understanding of the idea
of “slope” and the parameters that determine it. Students will also understand how the change in
slope affects the y-intercept of the line.
Suppose you are a participant of a scavenger hunt in a cornfield in Iowa. You are given the
coordinates to your starting point S = (12, 60), to your best friend’s location F = (-8,20), and to
your home base point H = (-30, -24).
Round 1: To complete the first leg of the hunt, you must find 8 items. Here are your clues.
Clue #1: Your first two items,  and , are located due east or due west of point H and point
F, respectively. The slope of the line through S and  is twice that of the line formed by S and
H.  is also located on the line through S and .
1. Where are  and  located?
2. What is the change in the x-values of S and H? S and F?
3. What is the change in the x-values of S and ? S and ?
4. What do you notice about the change in x-values of S and  compared to the change in
x-values of S and H? What do you notice about the change in x-values of S and  compared to
the change in x-values of S and F?
5. What do you notice about the change in the y-values of S and  and the change in the
y-values of S and B?
6. Find the y-intercept of the line through S and H and the y-intercept of the line through  and
H.
Clue #2: Your next two items,  and , are located due east or due west of H and F,
respectively. The slope of the line through S and is three times that of the line formed by S
and H.  is also located on the line through S and .
1. Where are  and  located?
2. What is the change in the x-values of S and H? S and F?
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
3. What is the change in the x-values of S and ? S and ?
4. What do you notice about the change in x-values of S and  compared to the change in
x-values of S and H? What do you notice about the change in x-values of S and 
compared to the change in x-values of S and F?
5. What do you notice about the change in the y-values of S and  and the change in the
y-values of S and B?
6. Find the y-intercept of the line through S and H and the y-intercept of the line through 
and H.
Clue #3: Your next items,  and , are located due east or due west of H and F, respectively.
The slope of the line through S and  is four times that of the line formed by S and H.  is
located on the line through S and .
1. Where are  and  located?
2. What is the change in the x-values of S and H? S and F?
3. What is the change in the x-values of S and ? S and ?
4. What do you notice about the change in x-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in x-values of S and  compared to
the change in x-values of S and F?
5. What do you notice about the change in the y-values of S and  and the change in the yvalues of S and B?
6. Find the y-intercept of the line through S and H and the y-intercept of the line through  and
H.
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
1. Using the graph and the information that you have gathered in your search for the first six
items, make a conjecture about the location of your last two items,  and , that are located
due east or due west of H and F, respectively, given that the slope of the line through S and 
is seven times that of the line formed by S and H and that  is on the line through S and .
Explain your reasoning.
2. Show that your conjecture is correct.
3. Using the information obtained from the first three clues complete the following table. Note
let m=slope of the line through S and H. What is the relation of n to the change in the slope?
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
(x1, y1) (x2, y2)
B=y-intercept
S=(12,60) H=(-30,-24)
36
S=(12,60) =(
)
S=(12,60) =(
)
=(
)
S=(12,60) =(
)
S=(12,60)
Let K = Change in
y-intercepts
Not applicable
B = y1 – n*m*x1
What is n?
Not applicable
Not applicable
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
60
S
50
40
30
20
F
10
-80
-60
-40
-20
20
40
60
80
-10
-20
H
-30
-40
-50
-60
Concluding questions:
1. As the slope is changed, what do you notice about the lines that you have graphed?
2. As the slope is changed, what do you notice about the y-intercepts of the lines?
3. Is it possible to change the slope enough to make a line that is vertical? Why or why not?
Congratulations! You have successfully completed the first leg of your journey!
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
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Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Round 2: You must find 8 items to complete this round.
Clue #1: Your first two items,  and , are located due east or due west of point H and point
F, respectively. The slope of the line through S and  is half that of the line formed by S and H.
 is also located on the line through S and .
Where are  and  located?
What is the change in the x-values of S and H? S and F?
What is the change in the x-values of S and ? S and ?
What do you notice about the change in x-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in x-values of S and  compared
to the change in x-values of S and F?
5. What do you notice about the change in the y-values of S and  and the change in the yvalues of S and B?
6. Find the y-intercept of the line through S and H and the y-intercept of the line through  and
H.
1.
2.
3.
4.
Clue #2: Your next two items,  and , are located due east or due west of H and F,
respectively. The slope of the line through S and  is one-third of the slope of the line formed
by S and H.  is also located on the line through S and .
1. Where are  and  located?
2. What is the change in the x-values of S and H? S and F?
3. What is the change in the x-values of S and ? S and ?
4. What do you notice about the change in x-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in x-values of S and  compared to
the change in x-values of S and F?
5. What do you notice about the change in the y-values of S and  and the change in the yvalues of S and B?
6. Find the y-intercept of the line through  and H.
Clue #3: Your next items,  and , are located due east or due west of H and F, respectively.
The slope of the line through S and  is one-fourth the slope of the line formed by S and H. 
is located on the line through S and .
1.
2.
3.
4.
Where are  and  located?
What is the change in the x-values of S and H? S and F?
What is the change in the x-values of S and ? S and ?
What do you notice about the change in x-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in x-values of S and  compared
to the change in x-values of S and F?
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
17
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
5. What do you notice about the change in the y-values of S and  and the change in the yvalues of S and B?
6. Find the y-intercept of the line through  and H.
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
1. Using the graph and the information that you have gathered in your search for the first six
items, make a conjecture about the location of your last two items,  and , that are
located due east or due west of H and F, respectively, given that the slope of the line through
S and  is one-seventh of the slope of the line formed by S and H and that  is on the line
through S and . Explain your reasoning.
2. Show that your conjecture is correct.
3. Using the information obtained from the first three clues complete the following table. Note
let m=slope of the line through S and H. What is the relation of n to the change in the slope?
(x1, y1) (x2, y2)
B=y-intercept
S=(12,60) H=(-30, -24)
36
S=(12,60) =(
)
S=(12,60) =(
)
=(
)
S=(12,60) =(
)
S=(12,60)
Let K=Change in
y-intercepts
Not applicable
B = y1 – n*m*x1
What is n?
Not applicable
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
18
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
100
90
80
70
60
S
50
40
30
20
F
10
-140
-120
-100
-80
-60
-40
-20
20
40
60
80
100
120
140
-10
-20
H
-30
-40
-50
-60
-70
-80
-90
-100
Concluding questions:
1. As the slope is changed, what do you notice about the lines that you have graphed?
2. As the slope is changed, what do you notice about the y-intercepts of the lines?
3. Is it possible to change the slope enough to make a line that is horizontal? Why or why
not?
4. Compare Round 1 and Round 2. How are the two situations similar? How are they
different?
Congratulations! You have successfully completed the second leg of your journey!
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
19
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Round 3: You must collect 8 items to complete this round.
Clue #1: Your first two items,  and , are located due north or due south of point H and
point F, respectively. The slope of the line through S and  is twice that of the line formed by S
and H.  is also located on the line through S and .
Where are  and  located?
What is the change in the y-values of S and H? S and F?
What is the change in the y-values of S and ? S and ?
What do you notice about the change in y-values of S and  compared to the change in yvalues of S and H? What do you notice about the change in y-values of S and  compared
to the change in y-values of S and F?
5. What do you notice about the change in the x-values of S and  and the change in the xvalues of S and B?
6. Find the y-intercept of the line through S and H and the y-intercept of the line  and H.
1.
2.
3.
4.
Clue #2: Your next two items,  and , are located due north or due south of H and F,
respectively. The slope of the line through S and  is three times that of the line formed by S
and H.  is also located on the line through S and .
Where are  and  located?
What is the change in the y-values of S and H? S and F?
What is the change in the y-values of S and ? S and ?
What do you notice about the change in y-values of S and  compared to the change in yvalues of S and H? What do you notice about the change in y-values of S and  compared
to the change in y-values of S and F?
5. What do you notice about the change in the x-values of S and  and the change in the xvalues of S and B?
6. Find the y-intercept of the line through  and H.
1.
2.
3.
4.
Clue #3: Your next items,  and , are located due north or due south of H and F,
respectively. The slope of the line through S and  is four times that of the line formed by S
and H.  is located on the line through S and .
Where are  and  located?
What is the change in the y-values of S and H? S and F?
What is the change in the y-values of S and ? S and ?
What do you notice about the change in y-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in y-values of S and  compared
to the change in y-values of S and F?
5. What do you notice about the change in the x-values of S and  and the change in the yvalues of S and B?
1.
2.
3.
4.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
20
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
6. Find the y-intercept of the line through  and H.
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
1. Using the graph and the information that you have gathered in your search for the first six
items, make a conjecture about the location of your last two items,  and , that are
located due north or due south of H and F, respectively, given that the slope of the line
through S and  is seven times that of the line formed by S and H and that  is on the line
through S and . Explain your reasoning.
2. Show that your conjecture is correct.
3. Using the information obtained from the first three clues complete the following table. Note
let m=slope of the line through S and H. What is the relation of n to the change in the slope?
(x1, y1) (x2, y2)
B=y-intercept
S=(12,60) H=(-30, -24)
36
S=(12,60) =(
)
S=(12,60) =(
)
=(
)
S=(12,60) =(
)
S=(12,60)
Let K = Change in
y-intercepts
Not applicable
B = y1 – n*m*x1
What is n?
Not applicable
Not applicable
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
21
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
120
100
80
60
S
40
F
20
-300
-250
-200
-150
-100
-50
50
H
100
150
200
-20
-40
-60
-80
-100
-120
-140
-160
-180
-200
-220
-240
-260
-280
Concluding questions:
1. As the slope is changed, what do you notice about the lines that you have graphed?
2. As the slope is changed, what do you notice about the y-intercepts of the lines?
3. Is it possible to change the slope enough to make a line that is vertical? Why or why not?
Congratulations! You have successfully completed the third leg of your journey!
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
250
22
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
Round 4: To complete this round, your will need to locate 8 items.
Clue #1: Your first two items,  and , are located due north or due south of point H and
point F, respectively. The slope of the line through S and  is half that of the line formed by S
and H.  is also located on the line through S and .
Where are  and  located?
What is the change in the y-values of S and H? S and F?
What is the change in the y-values of S and ? S and ?
What do you notice about the change in y-values of S and  compared to the change in yvalues of S and H? What do you notice about the change in y-values of S and  compared
to the change in y-values of S and F?
5. What do you notice about the change in the x-values of S and  and the change in the xvalues of S and B?
6. Find the y-intercept of the line through S and H and the y-intercept of the line through  and
H.
1.
2.
3.
4.
Clue #2: Your next two items,  and , are located due north or due south of H and F,
respectively. The slope of the line through S and  is one-third of the slope of the line formed
by S and H.  is also located on the line through S and .
Where are  and  located?
What is the change in the y-values of S and H? S and F?
What is the change in the y-values of S and ? S and ?
What do you notice about the change in y-values of S and  compared to the change in yvalues of S and H? What do you notice about the change in y-values of S and  compared
to the change in y-values of S and F?
5. What do you notice about the change in the x-values of S and  and the change in the xvalues of S and B?
6. Find the y-intercept of the line through  and H.
1.
2.
3.
4.
Clue #3: Your next items,  and , are located due north or due south of H and F,
respectively. The slope of the line through S and  is one-fourth the slope of the line formed
by S and H.  is located on the line through S and .
1.
2.
3.
4.
Where are  and  located?
What is the change in the y-values of S and H? S and F?
What is the change in the y-values of S and ? S and ?
What do you notice about the change in y-values of S and  compared to the change in xvalues of S and H? What do you notice about the change in y-values of S and  compared
to the change in y-values of S and F?
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
23
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
5. What do you notice about the change in the x-values of S and  and the change in the yvalues of S and B?
6. Find the y-intercept of the line through  and H.
Clue #4: On grid below, plot the points and the lines that are discussed in the first 3 clues.
1. Using the graph and the information that you have gathered in your search for the first six
items, make a conjecture about the location of your last two items,  and , that are
located due north or due south of H and F, respectively, given that the slope of the line
through S and  is one-seventh of the slope of the line formed by S and H and that  is
on the line through S and . Explain your reasoning.
2. Show that your conjecture is correct.
3. Using the information obtained from the first three clues complete the following table. Note
let m=slope of the line through S and H. What is the relation of n to the change in the slope?
(x1, y1) (x2, y2)
B=y-intercept
S=(12,60) H=(-30, -24)
36
S=(12,60) =(
)
S=(12,60) =(
)
=(
)
S=(12,60) =(
)
S=(12,60)
Let K = Change in
y-intercepts
Not applicable
B = y1 – n*m*x1
What is n?
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
24
Algebra I: Strand 2. Linear Functions; Topic 13. Scavenger Hunt (Student Version); Task 2.13.5
80
70
60
S
50
40
30
F
20
10
-120
-100
-80
-60
-40
-20
20
40
60
80
100
-10
H
-20
-30
-40
-50
-60
-70
-80
Congratulations! You have successfully completed the scavenger hunt!
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
120