Model changes in real life, such as fees, water volume, and temperature, using linear functions.
Example ①
A taxi fare is 500 yen for the first 1 km, with an additional 100 yen for each subsequent 1 km. Express the fare y yen for traveling x km as an equation in x (x ≧ 1).
Answer: y = 500 + 100(x−1) = 100x + 400. y = 100x + 400
A taxi fare is 500 yen for the first 1 km, with an additional 100 yen for each subsequent 1 km. Express the fare y yen for traveling x km as an equation in x (x ≧ 1).
Answer: y = 500 + 100(x−1) = 100x + 400. y = 100x + 400
Key Points
- A constant rate of change → a linear function (slope = rate of change)
- The initial value (the value when x=0 or at the reference point) is the intercept
- Two conditions determine the equation
Practice Problems
- A tank contains 20 L of water. Water is drained at a rate of 3 L per minute. Express the amount of water y L after x minutes as an equation, and find how many minutes it takes for the tank to become empty.
Answers and Explanations
- Answer: y=−3x+20. y=0→x=20/3≒6.67. Approximately 6 minutes 40 seconds later (6 minutes 40 seconds later).