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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: A canoe rents for $15 per hour. Which quantity is independent — hours or total cost? The hours of rental is independent; the total cost depends on it. Say the pattern in words: the total cost equals $15 times the number of hours. Let h = hours rented and c = total cost. What equation matches? c = 15h. Check it: a 3-hour rental is 15 × 3 = 45 dollars, and a 5-hour rental is 15 × 5 = 75 dollars. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartIn the ordered pair (x, y), which value is graphed along the horizontal axis?

   1. Ax
   2. By
   3. CBoth of them
   4. DNeither one

   How do you know?
3. 3

   Warm restartA table pairs x = 1, 2, 3 with y = 3, 6, 9. Which ordered pair is in the table?

   1. A(2, 6)
   2. B(6, 2)
   3. C(2, 3)
   4. D(3, 2)

   How do you know?
4. 4

   Warm restartOn a graph of hours worked and money earned, which axis shows the independent variable?

   1. AThe horizontal axis
   2. BThe vertical axis
   3. CEither axis works
   4. DNeither axis

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughIn Diamond's situation, what should be the independent variable in both equations?

   1. Athe number of songs
   2. Bthe total cost
   3. Cthe price per song
   4. Dthe type of service (purchase or stream)

   Why is that the answer?
2. 6

   Think it throughWhy does Diamond need TWO separate equations instead of one equation for both options?

   1. APurchasing and streaming likely follow different cost rules (such as a per-song price vs. a flat rate), so each relationship between songs and cost is different
   2. BThe number of songs is different for each option
   3. COne equation can only have one variable
   4. DStreaming has no relationship between songs and cost

   How do you know? Give a second reason as well.
3. 7

   Think it throughOnce Diamond has both equations, how does she use them to decide which option is better?

   1. ASubstitute the same number of songs into both equations and compare the two total costs
   2. BAdd the two equations together to find one combined cost
   3. CPick whichever equation has the smaller numbers written in it, without solving anything
   4. DGraph only one equation and assume the other follows the same line

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelRecreation World charges $24.95 per month, and the table shows the cost growing by exactly $24.95 every row. Why is the equation c = 24.95m correct, but c = 24.95 + m would be wrong?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• The total for 2 months is $49.90
• The total for 3 hours is $45
• The total for 4 months is $99.80
• The total for 5 hours is $75
• The rate is $24.95 per month
• The rate is $15 per hour
• 10 months costs $249.50
• 2 hours costs $30

Use the words

Fill each blank with a word from the bank.

• A mathematical sentence with an equals sign is an ___.
• A letter standing for a quantity that can change is a ___.
• A fixed amount of one quantity for every one unit of the other is a ___.
• To show a relationship with a table, graph, or equation is to ___ it.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: Writing the equation with addition — c = 24. 95 + m — instead of multiplication.
2. 10

   Say moreYou sorted cards between the gym equation (c = 24.95m) and the canoe equation (c = 15h). How did you decide where '2 hours costs $30' belonged?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A flyer for Recreation World shows a monthly membership fee of $24.95. Below it is a table: 1 month, $24.95. 2 months, $49.90. 3 months, $74.85. 4 months, $99.80. 10 months, $249.50.

   Show your work

Last check

These two come from Lesson 9.2. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Recreation World charges $24.95 per month. Let m = number of months and c = total cost. Which equation represents the relationship?

   1. Ac = 24.95m
   2. Bc = 24.95 + m
   3. Cm = 24.95c
   4. Dc = m ÷ 24.95

   Explain your choice.
2. 13

   From Lesson 9.2Explain your thinking — On the football ticket graph, what does the point (3, 135) represent?

   1. A3 tickets cost a total of $135
   2. B135 tickets cost a total of $3
   3. C3 tickets cost $135 each
   4. DThe game lasts 135 minutes

   How do you know?
3. 14

   From Lesson 9.2A point on the graph is located at (4, x). Based on the interest rate, what value of x makes this point correct?

   1. A$105
   2. B$78.75
   3. C$855
   4. D$131.25

   How do you know?

Be honest — this tells your teacher what to do next