Linear Functions in Real-Life Situations

A linear function shows a relationship where one quantity changes at a constant rate.

Basic Form

y = mx + b

• x = input or amount that changes

• y = total result

• m = rate of change

• b = starting value or fixed fee

Simplified Examples

1. Laundry Shop

• Fixed fee: ₱30

• Cost per kilogram: ₱45

• Equation: y = 45x + 30

• Meaning: Total cost = ₱45 for each kilogram + ₱30 service fee.

2. Printing Shop

• Fixed fee: ₱15

• Cost per page: ₱3

• Equation: y = 3x + 15

• Meaning: Total cost = ₱3 for each page + ₱15 setup fee.

3. Salesperson

• Monthly salary: ₱10,000

• Commission: ₱500 per appliance

• Equation: y = 500x + 10,000

• For 8 appliances:

  • y = 500(8) + 10,000

  • y = ₱14,000

• Answer: The salesperson earns ₱14,000.

4. Sari-Sari Store

• Price per bottle: ₱15

• Equation: y = 15x

• For 24 bottles:

  • y = 15(24)

  • y = ₱360

• Answer: The store receives ₱360.

5. Part-Time Student

• Pay: ₱120 per hour

• Work schedule: 6 hours per day for 2 days

• Total hours: 6 × 2 = 12

• Earnings: ₱120 × 12 = ₱1,440

• Answer: The student earns ₱1,440.

6. Worker

• Pay: ₱400 per day

• Equation: y = 400x

• Meaning: Total earnings = ₱400 multiplied by the number of days worked.

7. Bicycle

• Speed: 12 kilometers per hour

• Equation: y = 12x

• Meaning: Distance = 12 multiplied by the number of hours traveled.

Quick Reminder

To solve a linear-function problem:

1. Find the rate or amount per unit.

1. Find any fixed starting value.

1. Write the equation.

1. Substitute the given value for x.

1. Calculate y, the total result.