8.2. Double Line Graphs http://www.ck12.org
a. Explain the slopes of the line segments for Christopher’s graph.
b. Explain the slopes of the line segments for Jack’s graph.
c. Are there any negative slopes? What does this mean?
d. Where is the highest point on Christopher’s graph? What does this tell you?
e. Where is the highest point on Jack’s graph? What does this tell you?
f. Can you provide some reasons for the shape of Jack’s graph?
g. Can you provide some reasons for the shape of Christopher’s graph?
Answer:
a. The slope of the line segments for Christopher’s graph (red) are positive for the first 5 weeks, meaning he was
increasing his sales each week. This is also true from weeks 6 to 7. From weeks 5 to 6 and weeks 7 to 8, the slopes
were decreasing, meaning there was a decrease in sales.
b. The same trend that is seen for Christopher’s graph (red) is also seen for Jack’s graph (blue). The slope of the line
segments for Jack’s graph (blue) are positive for the first 5 weeks, meaning he was increasing his sales each week.
This is also true from weeks 6 to 7. From weeks 5 to 6 and weeks 7 to 8, the slopes were decreasing, meaning there
was a decrease in sales.
c. Negative sales from weeks 5 to 6 and weeks 7 to 8 (for both boys) mean there was a decrease in sales during these
2-week periods.
d. The highest point on Christopher’s graph occurred in week 7, when he sold 65 glasses of lemonade. This must
have been a very good week−nice and hot!
e. The highest point on Jack’s graph occurred in week 5, when he sold 74 popsicles. This must have been a very hot
week as well!
f. Popsicles are a great food when you are warm and want a light snack. You can see how as the summer became
hotter, the sales increased. Even in the weeks where it looks like Jack had a decrease in sales (maybe a few rainy
days occurred, or it was not as hot), his sales still remained at a good level.
g. Lemonade is a very refreshing drink when you are warm. You can see how as the summer became hotter, the
sales increased. Even in the weeks where it looks like Christopher had a decrease in sales (maybe a few rainy days
occurred, or it was not as hot), his sales still remained at a good level, just as Jack’s sales did.
Practice
- Scott is asked to track his daily video game playing. He gets up at 7 A.M. and plays for 1 hour. He then
eats his breakfast and gets ready for school. He runs to catch the bus at 8:25 A.M. On the bus ride (about 35
minutes), he plays his IPOD until arriving for school. He is not allowed games at school, so he waits for the
bus ride home at 3:25 P.M. When he gets home, he does homework for 1 hour and plays games for 1 hour
until dinner. There are no games in the evening. Michael gets up at 7:15 A.M., eats breakfast, and gets ready
for school. It takes him 30 minutes to get ready. He then plays games until he goes to meet the bus with Scott.
Michael is in Scott’s class, but he has a free period from 11:00 A.M. until 11:45 A.M., when he goes outside to
play a game. He goes home and plays his 1 hour of games immediately, and he then works on his homework
until dinner. He, like Scott, is not allowed to play games in the evening. The following broken-line graph was
drawn for each set of data. Explain why the graph is wrong.