1. Determine whether or not the following graphs represent two quantities that are proportional to each other.
Explain your reasoning.
b.
Donated Money vs. Donations Matched
Age vs. Admission Price
by Benefactor
a.
500
400
5
Donations Matched by Benefactor ($)
Admission Price (5)
200
2
100
1
0
o
7
0
0
8
3
2
400
500
100 200 300
Money Donated
Age (years)
C.
Extra Credit vs. Number of Problems
Extra Credit Points
20
18
16
14
12
10
12 3 4 5 6
Number of Problems Solved

The first sentence is not true in general. Consider the equation . There are no solutions. Now consider . There is only one solution, .

But whatever. You're asked to demonstrate that has two solutions (which is true; the right hand side must be a positive integer in order to have two solutions). This follows immediately from the definition of absolute value, which says



So suppose . Then



Now suppose . Then



So two solutions to are .