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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: The tram travels 1,200 feet every minute. Which quantity is independent — time or distance? Time is independent, so our pairs look like (minutes, feet): (1, 1200), (2, 2400), (5, 6000). The ascent takes 15 minutes, so the last point is (15, 18000) — because 15 times 1,200 is 18,000 feet. Each point means: after THIS many minutes, the tram has traveled THIS many feet. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartSongs cost $2 each. Which is the independent variable?

   1. AThe number of songs bought
   2. BThe total cost
   3. CThe $2 price
   4. DThe music store

   How do you know?
3. 3

   Warm restart"The longer you run, the more calories you burn." Which is the dependent variable?

   1. ACalories burned
   2. BMinutes run
   3. CThe runner
   4. DThe distance

   How do you know?
4. 4

   Warm restartA plant grows taller each day. Which sentence is correct?

   1. AHeight depends on the number of days
   2. BThe number of days depends on height
   3. CNeither one depends on the other
   4. DBoth are independent variables

   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 throughOn Nakai's graph, which variable is plotted on the independent axis (x-axis)?

   1. Ayears
   2. Binterest earned
   3. Cprincipal amount
   4. Daccount balance

   Why is that the answer?
2. 6

   Think it throughWhy does the graph rise by the same amount every year instead of curving upward more steeply over time?

   1. ANakai earns simple interest — the same $26.25 each year, calculated only on the original $750 principal
   2. BNakai earns compound interest, which grows faster each year
   3. CThe interest rate increases by 3.5% every year
   4. DNakai deposits an extra $26.25 into the account every year

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

   Think it throughA 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

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

   Back to the modelFootball tickets cost $45 each: 1 ticket is $45, 2 tickets are $90, 3 tickets are $135. When you write the ordered pair for 3 tickets, which number goes first — 3 or 135 — and why?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• (2, 90) is a point on the graph
• (3, 135) is a point on the graph
• (4, 190) is a point on the graph
• (1, 55) is a point on the graph
• (5, 225) is a point on the graph
• As tickets increase, the total cost increases
• (6, 260) is a point on the graph
• The total cost is 45 times the number of tickets

Use the words

Fill each blank with a word from the bank.

• A picture on the coordinate plane showing how two quantities relate is a ___.
• A list of matched pairs that shows a relationship in numbers is a ___ ___ ___.
• Two numbers written (x, y) that name one point are an ___ ___.
• Each number line framing a graph, labeled with a quantity, is an ___.

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: Reversing the coordinates of a point — writing (cost, tickets) instead of (tickets, cost).
2. 10

   Say moreYou sorted cards like '(4, 190) is a point on the graph' into matches and non-matches for cost = 45 × tickets. How did you check each one?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A ticket to a college football game costs $45. Next to the ticket is a table: 1 ticket, $45. 2 tickets, $90. 3 tickets, $135. Beside the table is a graph with points climbing up and to the right.

   Show your work

Last check

These two come from Lesson 9.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain 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

   Explain your choice.
2. 13

   From Lesson 9.1Explain your thinking — A dog walker charges by the hour. Which sentence is correct?

   1. AThe total charge depends on the number of hours, so hours is the independent variable.
   2. BThe number of hours depends on the total charge, so the charge is the independent variable.
   3. CBoth quantities are independent variables.
   4. DNeither quantity depends on the other.

   How do you know?
3. 14

   From Lesson 9.1The shop makes 20 pizzas in a week. Which of these does NOT depend on the number of pizzas sold?

   1. Athe total cost of cheese
   2. Bthe total cost of sauce
   3. Cthe number of employees
   4. Dthe total spent on cheese and sauce combined

   How do you know?

Be honest — this tells your teacher what to do next