Lesson 3: Introduction to Graphing Problem Solving Assignment solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 1 of 4
1. The manufacturer of the video game Spaced Out recorded data of the
number of games sold on a given day as the price of the game changed.
Date Price # Sold
Jan. 3 $17 2530
Feb. 5 $20 2000
Mar. 10 $22 1920
Jun. 6 $27 1650
Aug. 25 $19 2010
Nov. 29 $30 1700
a) Graph the data with price on the horizontal axis and number sold on the vertical axis.
b) What trends do you notice between the price of the games and the number of games sold?
Generally, as the price goes up, the sales go down. The lower
the price, the more video games are sold.
84 12 16 20 24 28 32 36 40 44
1200
600
1800
2400
3000
Lesson 3: Introduction to Graphing Problem Solving Assignment solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 2 of 4
c) Does this trend make sense to you? Explain your answer.
Yes, this makes a lot of sense. Usually if things are more expensive, then fewer items are purchased. But if the price is
decreased, then the sales increase.
2. Find an equation of the circle pictured below.
If each of the gridlines represents one unit, then the Center is
at ( )5,6− , and the radius is 4 units.
Then the equation of the circle is:
( )( ) ( )
( ) ( )
2 2 2
2 2
5 6 4
5 6 16
x y
x y
− − + − =
+ + − =
C
Lesson 3: Introduction to Graphing Problem Solving Assignment solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 3 of 4
3. For the circle pictured above, a student says that the equation of the
circle could be ( ) ( )2 2 210 12 8x y+ + − = . Do you agree or disagree?
Explain your answer.
Agree. If each of the gridlines represents 2 units, then the
Center is at ( )10,12− , and the radius is 8 units.
Then the equation of the circle is:
( )( ) ( )
( ) ( )
2 2 2
2 2 2
10 12 8
10 12 8
x y
x y
− − + − =
+ + − =
4. Are (19, -7), (3, 5), and (12, 17) the coordinates of a right triangle?
Show all of your calculations and justify your answer.
Let x be the distance between the points ( )3,5 and ( )12,17 .
Let y be the distance between the points ( )12,17 and ( )19, 7− .
Let z be the distance between the points ( )19, 7− and ( )3,5 .
( ) ( )2 22
2 2 2
2
2
12 3 17 5
9 12
81 144
225
15
x
x
x
x
x
= − + −
= +
= +
=
=
( ) ( )
( )
2 22
22 2
2
2
19 12 7 17
7 24
49 576
625
25
y
y
y
y
y
= − + − −
= + −
= +
=
=
( ) ( )
( )
2 22
22 2
2
2
19 3 7 5
16 12
256 144
400
20
z
z
z
z
z
= − + − −
= + −
= +
=
=
If the triangle is a right triangle, then y is the hypotenuse
(since it has the greatest length). If the triangle is a right
triangle, then 2 2 2x z y+ = .
Lesson 3: Introduction to Graphing Problem Solving Assignment solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 4 of 4
?2 2 2
?2 2 2
?
?
15 20 25
225 400 625
625 625
x z y+ =
+ =
+ =
= �
Since 2 2 2x z y+ = , the given coordinates are the coordinates of
a right triangle.
