Lesson 6: Identifying Proportional and Non-Proportional Relationships in Written Descriptions

1. Proportional relationship in words
   If the description shows a constant multiplier, it is proportional.

• Example: “A taxi charges $3 per mile.” → This is proportional (y = 3x).

2. Non-proportional relationship in words
   If the description adds or subtracts an extra amount, it is not proportional.

• Example: “A taxi charges $3 per mile plus a $2 starting fee.” → Not proportional (y = 3x + 2).

3. Check for proportionality

• Does the situation start at zero? (If x = 0, does y = 0?)
• Is there a constant rate per unit?

Part B

1. A babysitter charges $10 for each hour she works.
Step 1: At 0 hours, cost = 0.
Step 2: Constant rate = $10/hour.
Answer: Proportional.

2. A taxi company charges $3 per mile plus $5 at the start of the ride.
Step 1: At 0 miles, cost = $5.
Step 2: Does not start at 0.
Answer: Not proportional.

3. A factory makes 20 pencils every minute.
Step 1: At 0 minutes, pencils = 0.
Step 2: Constant = 20/minute.
Answer: Proportional.

4. A music subscription costs $5 to join and $2 each month.
Step 1: At 0 months, cost = $5.
Step 2: Extra fee added.
Answer: Not proportional.

5. A runner jogs 4 miles every hour.
At 0 hours, 0 miles. Constant = 4.
Answer: Proportional.

6. A plumber charges $50 per hour plus a $20 service fee.
At 0 hours, cost = $20.
Answer: Not proportional.

7. A bakery sells 3 muffins for $2.
At 0 muffins, $0. Constant = $2/3 muffin.
Answer: Proportional.

8. A gym charges $30 each month and a one-time $10 fee.
At 0 months, cost = $10.
Answer: Not proportional.

9. A bike rental is $8 per hour.
At 0 hours, $0. Constant = 8.
Answer: Proportional.

10. A parking garage is $2 per hour plus $5 flat entry fee.
At 0 hours, $5.
Answer: Not proportional.

11. A school bus travels 40 miles every hour.
At 0 hours, 0 miles. Constant = 40.
Answer: Proportional.

12. A movie theater charges $12 per ticket and $3 for 3-D glasses.
At 0 tickets, $3.
Answer: Not proportional.

13. A cook uses 2 cups of flour for each batch of cookies.
At 0 batches, 0 flour. Constant = 2.
Answer: Proportional.

14. A babysitter charges $15 per hour plus $5 for travel.
At 0 hours, $5.
Answer: Not proportional.

15. A swimming pool fills at 200 gallons per hour.
At 0 hours, 0 gallons. Constant = 200.
Answer: Proportional.

16. A soccer team pays $100 for uniforms plus $10 per player.
At 0 players, $100.
Answer: Not proportional.

17. A farmer plants 50 trees per acre.
At 0 acres, 0 trees. Constant = 50.
Answer: Proportional.

18. A phone company charges $40 per month plus $100 for the phone.
At 0 months, $100.
Answer: Not proportional.

19. A chef uses 3 eggs for every cake.
At 0 cakes, 0 eggs. Constant = 3.
Answer: Proportional.

20. A taxi costs $2 per mile.
At 0 miles, $0. Constant = 2.
Answer: Proportional.