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```Name___________________________________________________ Applications of Graphing
Homework
Math 8
The Ohio Theater publishes a playbill for each play, which helps offset production costs. The
playbill contains information and pictures of cast members as well as interviews with the
producer and director.
The owner of the theater must consider how much to charge for each playbill, and how much
money can be raised.
1. The accountant for the production has researched previous years’ sales records and
organized the results in the following table. Graph the data on the grid below.
Theater Playbill Sales
Number of
Playbill
Sold
\$2.50
1,625
\$4.00
1,250
\$5.00
1,000
\$5.50
875
\$7.50
375
2000
Number of playbills sold
Playbill
Price
2375
1500
1000
500
2. Draw a line through the points on your graph.
2
4
6
2 playbill2 price
8
2
3. The relationship between the price and the number of playbills sold is linear. Justify this
statement using both the table and the graph.
4. Determine the slope of the line through
the points.
5. Describe the meaning of the slope in this
problem situation.
10
2
6. Use the data in the table and the graph to
determine the y-intercept of the line
through the data points.
7. Describe the meaning of the y-intercept in
this problem situation.
8. Write the equation of the line through the
data points in slope-intercept form.
9. Is the relationship between the price of
the playbills and the number of playbills
sold directly proportional? Justify your
response.
Assume the slope of the line was changed to -450.
10. Write the equation that could be used to
represent this new relationship between
the price of the playbills and the number
of playbills sold.
11. Describe any changes in the graph that
would result from this change in the slope.
Number of T-shirt Sold
The Band Boosters Club at Newland High School
1400is planning to sell t-shirts to raise money for
new instruments. The shirts will be designed with the school colors and mascot on the front.
The Boosters must consider how much to charge
1200for each t-shirt, and how much money can
be raised
1000
The Band Booster Treasurer has researched previous years’ sales records and organized the
results in the following table. Graph the data on
the grid below.
800
Band Boosters T-Shirt
Sales
Number
T-shirt
of T-Shirts
Price
Sold
\$1.50
1350
\$3.00
1200
\$4.50
1050
\$6.50
850
\$9.00
600
600
400
0
200
2
4
2
6
8
2
2
T-shirt Price
10
2
12
2
12. Draw a line through the points on your graph.
13. The relationship between the price and the number of t-shirts sold is linear. Justify this
statement using both the table and the graph.
14. Determine the slope of the line through
the points.
15. Describe the meaning of the slope in this
problem situation.
16. Use the data in the table and the graph to
determine the y-intercept of the line
through the data points.
17. Describe the meaning of the y-intercept in
this problem situation.
18. Write the equation of the line through the
data points in slope-intercept form.
19. Is the relationship between the price of
the t-shirts and the number of t-shirts sold
directly proportional? Justify your
response.
Assume the slope of the line was changed to -75.
20. Write the equation that could be used to
represent this new relationship between
the price of the t-shirts and the number of
t-shirts sold.
21. Describe any changes in the graph that
would result from this change in the slope.
480
Number of Ornament Sold
420
Each hospital has an auxiliary group, which is a volunteer
group whose focus is to raise money
0
to help fund projects at the hospital. The auxiliary group at Mercy Hospital would like to sell
360
holiday ornaments to raise funds to help purchase
The chairman of the finance committee has researched
previous years’ sales records and
300
organized the results in the following table. Graph the data on the grid below.
Mercy Hospital
Auxiliary Holiday
Ornament Sales
Number of
Ornament
Ornaments
Price
Sold
\$3.50
345
\$4.50
315
\$6.00
270
\$8.50
195
\$10.00
150
240
180
120
60
2
4
2
6
8
2
2
Ornament Price
10
2
12
2
22. Draw a line through the points on your graph.
23. The relationship between the price and the number of ornaments sold is linear. Justify this
statement using both the table and the graph.
24. Determine the slope of the line through
the points.
25. Describe the meaning of the slope in this
problem situation.
26. Use the data in the table and the graph to
determine the y-intercept of the line
through the data points.
28. Write the equation of the line through the
data points in slope-intercept form.
27. Describe the meaning of the y-intercept in
this problem situation.
29. Is the relationship between the price of
the ornaments and the number of
ornaments sold directly proportional?