x

6 =

8 point problems

x

8 =

10 point problems

x 10 =

12 point problems

x 12 =

Points Attempted

Points Earned (for teacher use only)

Final Grade:

Your goal is to earn 100 points. If you answer a question correctly you will be awarded the number of points that problem was assigned. You must solve at least one problem from each category. Number of problems solved 6 point problems

x

6 =

8 point problems

x

8 =

10 point problems

x 10 =

12 point problems

x 12 =

Points Attempted

Final Grade:

Points Earned (for teacher use only)

Linear Relationships 100 Point Challenge

6 Point Problems Write the equation that represents the data in the table. 6a.

6c.

6e.

x

Process

y

6b.

x

Process

y

-8

4

-5

29

0

-2

-2

11

4

-5

0

-1

12

-11

3

-19

16

-14

6

-37

x

Process

y

6d.

x

Process

y

-4

-14

-3

-11

-2

-7

-1

-1

1

3.5

2

14

3

10.5

6

34

8

28

10

54

x

Process

y

6f.

x

Process

y

-3

1

-4

-15

0

0

-1

-9

3

-1

1

-5

6

-2

5

3

9

-3

8

9

Linear Relationships 100 Point Challenge

8 Point Problems 8a.

Marissa has $100 on her Sonic™ gift card. Every day she buys the same drink. The graph below represents the balance on the gift card, y, after each drink purchase, x.

Use the table below to determine the rate of change. Number of Drinks

Gift Card Balance

Process

Which of the following is NOT the rate of change in the situation?

8b.

1 2

A.

2

B.

– 2.5

C. D.

10 2 5 2

Look at the description of an equation below. The y-value is seven more than twice the value of x. Which of the following equations represents this description?

8c.

A.

y 7x 2

C.

y 72 x

B.

y 2x 7

D.

y 7(2x)

There is a linear relationship between a salesperson’s sales and her weekly income. She earns a base salary plus a commission on her sales. If her sales are $200, her income is $500, and if her sales are $1,200 her income is $600. What equation can be used to model this relationship?

8d.

The cost in dollars of a loaf of bread in a bakery is equal to 2 minus 0.25 times the number of days since it was baked. Use the table below to represent the relationship between days and cost of a loaf of bread. Number of Days

Cost of Loaf of Bread $1.75

Process

(Since Baked)

3 $0.50 8 Is there a point at which the linear relationship between days and dollars no longer makes sense? Explain. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 8e.

The table below shows the number of tickets purchased for a play and their total cost. Number of Tickets 1 2 3 4

Total Cost $7 $12 $17 $22

Describe (in words) the total amount paid in dollars based on the number of tickets. The amount paid is ___________________________ the number of tickets _________________.

8f.

Which description corresponds to the relationship shown in the table below?

A. B. C. D.

earning earning earning earning

Hours

5

10

15

20

Pay

$50

$90

$130

$170

$10 per hour $8 per hour plus a $10 bonus $7 per hour plus a $15 bonus $9 per hour

Linear Relationships 100 Point Challenge

10 Point Problems 10a.

Hailey entered an equation into y1 of a graphing calculator. The graph of the equation is shown below.

Hailey wrote the following statements about the equation. I. II. III. IV.

The The The The

equation equation equation equation

has a constant that is positive. has a negative rate of change. is non-proportional. is linear.

Which of the statements shown above is true about the equation? A. B. 10b.

I and IV only II and III only

C. D.

II, III and IV only All of the above

The table below shows the total cost of potatoes, y, based on the number of pounds purchased, x. Number of Pounds 2 4 7 10

Total Cost $3.00 $6.00 $10.50 $15.00

Which of the following shows the correct keystrokes to enter the first point from the table into the list on your graphing calculator? A.

STAT 1:EDIT, ENTER Enter 2 into L1 and 3 into L2

C.

2nd STAT 1:EDIT, ENTER Enter 2 into L1 and 3 into L2

B.

2nd Y= 1:PLOT, ENTER ON, ENTER

D.

Y= Enter 2x + 3 2nd GRAPH

10c.

10d.

Jacob is comparing the total cost of two different lawn services. Better Lawns charges $25 per hour. Best Lawns charges $20 per hour plus a $5 charge for gasoline. Which of the following calculator screens correctly shows the equations that represent both situations? A.

C.

B.

D.

Elmer enters two equations into his graphing calculator. He puts one equation in y1 and the other one in y2. He looks at the tables of the two equations.

Which of the following statements is NOT true about the equations?

10e.

A. B.

The equation in y1 is proportional. The equation in y2 is non-proportional.

C.

The equation in y2 has a constant of proportionality of

D.

Both equations represent linear relationships.

1 . 2

Look at the graph below.

Place a check next to each statement that correctly describes the relationship shown on the graph. _____ _____ _____ _____ _____ _____

Multiplicative Additive Proportional Non-Proportional Linear Has a constant rate of change

Linear Relationships 100 Point Challenge

12 Point Problems 12a.

Arturo is comparing the distance traveled of two runners in the same race. Runner A runs at a pace of 5 miles per hour. Runner B runs at a pace of 4 miles per hour but started the race 2 miles past the starting line. Describe how you could use a graphing calculator to represent this situation on a graph and a table. Include the keystrokes necessary to enter the information into the calculator. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

12b.

Cory uses a dryer at the local Laundromat that still has some time left. He adds some quarters to the meter. The table below represents the number of minutes left based on the number of quarters inserted into the dryer. Number of Quarters 2 6 10 12 20

Process

Number of Minutes 18 46 74 88 144

Use the table above to determine the equation that would represent the situation. y = ___________________ How many minutes were on the meter before he added quarters to the dryer? __________ How many minutes would be added to the dryer if Cory added only 1 quarter? __________ How many minutes would be added to the meter if Cory added 3 quarters? __________ How many quarters did Cory add if the total number of minutes on the dryer was 60? _________

12c.

Molly orders necklace kits online. The cost of the necklace kits can be represented by a linear relationship. Molly’s order of 3 kits cost $12.50. Another order of 5 kits cost $17.50. Molly decides that the kits cost $5 each. Is she correct? Explain.

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

12d.

Luis will participate in a walkathon for charity. He received a pledge from his aunt, and the table shows the relationship between the miles walked by Luis and the amount his aunt pledged. Miles Walked Amount Pledged

1

2

3

4

5

6

$31.50

$33.00

$34.50

$36.00

$37.50

$39.00

Luis’s mother decides to also pledge $15 plus an additional $3 per mile. If Luis wants to earn the same amount from his mother and his aunt, how far must he walk? What is the amount he will earn from each person?