Variable Relationships — Worksheet

Variable Relationships

Worksheet

Open the Variable Relationships module. Choose the situation and set the independent value described in each question. Read the equation, the table, and the graph to answer below.

Name: Date:

Part A: Reading the rule

1. In Speed mode the rule is d = 60t. Set the independent value t = 2. The module shows d = 60 × 2 = 120 miles. Which equation expresses the rule? 1 pt
  • d = 120t
  • d = 60t
  • t = 60d
  • d = 2t
2. Switch to Cost mode. Apples cost 4 dollars per pound, so the rule is c = 4q. Set q = 5. What is the cost in dollars? 1 pt
Answer:
3. Switch to Wages mode and set h = 3. The readout shows w = 15 × 3 = 45 dollars. Which equation relates wages w to hours h? 1 pt
  • w = 45h
  • h = 15w
  • w = 15h
  • w = 3h

Part B: Completing the table

4. In Speed mode the table's left column lists t from 0 to 10. Which row shows a distance of 180 miles? 1 pt
  • t = 3
  • t = 4
  • t = 6
  • t = 30
5. Switch to Cost mode. Find the row for q = 7. What is c in that row? 1 pt
Answer:
6. In Speed mode, one row of the table has t = 9. What is d in that row? 1 pt

Part C: Matching an equation to a graph

7. Switch to Cost mode and set q = 2. The marked point sits at (2, 8). Which equation matches this line? 1 pt
  • q = 4c
  • c = 2q
  • c = 4q
  • c = 8q
8. Switch to Wages mode. The line passes through the point (4, 60). Which equation matches it? 1 pt
  • w = 15h
  • w = 4h
  • w = 60h
  • h = 15w

Part D: Independent and dependent variables

9. In Speed mode, which quantity is the independent variable? 1 pt
  • distance d, because the car moves
  • time t, because it is the value you choose
  • the speed 60, because it never changes
  • neither quantity, because both change
10. In Speed mode, turn Swap axes on and set t = 4. The readout beside the point now shows (240, 4). What is the first number in that pair? 1 pt
Answer:
11. In Wages mode, what happens when you turn Swap axes on? 1 pt
  • The rule changes from w = 15h to h = 15w.
  • The independent and dependent variables trade axes, but the rule w = 15h is unchanged.
  • The job pays a different rate.
  • The table stops matching the graph.

Part E: Reasoning

12. Explain which quantity is independent and which is dependent in the wages situation w = 15h, and why. Use the words input and output in your answer. 2 pts
13. Turn on Swap axes in Cost mode and look at all three views. Describe what changed and what stayed the same. Does c = 4q still describe the relationship? Explain. 2 pts