Real-world examples of linear relationships in everyday life (Algebra 1 applications).

📚 Real-World Examples of Linear Relationships

Linear relationships are everywhere! They show up whenever there's a constant rate of change. Here's a quick guide to help you spot them:

• 🚶 Walking Speed: 🚶‍♀️ If you walk at a constant speed, the distance you cover is linearly related to the time you spend walking. For example, if you walk 3 miles per hour, the equation is $d = 3t$, where $d$ is the distance and $t$ is the time.
• ⛽ Gasoline Consumption: 🚗 The amount of gasoline your car uses is often linearly related to the distance you drive. If your car gets 30 miles per gallon, the equation is $g = \frac{d}{30}$, where $g$ is the gallons of gas used and $d$ is the distance.
• 💸 Simple Interest: 🏦 If you deposit money in a savings account with simple interest, the amount of money you have grows linearly over time. The formula is $A = P(1 + rt)$, where $A$ is the final amount, $P$ is the principal, $r$ is the interest rate, and $t$ is the time.
• 🍎 Cost of Items: 🛒 If each item costs the same amount, the total cost is linearly related to the number of items. If apples cost $1.50 each, the total cost $C$ for $n$ apples is $C = 1.50n$.
• 🌡️ Temperature Conversion: 🌡️ Converting Celsius to Fahrenheit (or vice versa) is a linear relationship. The formula to convert Celsius to Fahrenheit is $F = \frac{9}{5}C + 32$.

Practice Quiz

1. Question 1: A taxi charges an initial fee of $2.50 plus $0.20 per mile. Which equation represents the total cost (C) as a function of miles driven (m)?
   1. A) C = 0.20 + 2.50m
   2. B) C = 2.50 + 0.20m
   3. C) C = 2.70m
   4. D) C = 2.30m
2. Question 2: Sarah is saving money at a constant rate. After 3 weeks, she has $45, and after 5 weeks, she has $75. What is her weekly savings rate?
   1. A) $10
   2. B) $15
   3. C) $20
   4. D) $25
3. Question 3: A phone company charges a monthly fee of $30 plus $0.05 per minute of usage. If your bill was $35, how many minutes did you use?
   1. A) 50 minutes
   2. B) 100 minutes
   3. C) 150 minutes
   4. D) 200 minutes
4. Question 4: A rental car costs $25 per day plus a one-time fee of $50. If you rent the car for 4 days, what is the total cost?
   1. A) $75
   2. B) $100
   3. C) $150
   4. D) $175
5. Question 5: The temperature in Celsius is 25 degrees. What is the equivalent temperature in Fahrenheit, using the formula $F = \frac{9}{5}C + 32$?
   1. A) 45°F
   2. B) 68°F
   3. C) 77°F
   4. D) 82°F
6. Question 6: A small business’s profit increases linearly each month. In January, the profit was $1000 and in March, it was $1500. Assuming no changes, what will the profit be in June?
   1. A) $2000
   2. B) $2250
   3. C) $2500
   4. D) $2750
7. Question 7: A hot dog vendor sells hot dogs for $3 each. If his daily expenses are $50, how many hot dogs must he sell to break even?
   1. A) 15
   2. B) 16
   3. C) 17
   4. D) 18