Use linear functions in various contexts, such as speed, area, and cost.
Example ① (Cost)
The basic electricity charge is 1000 yen, and the charge is 25 yen per 1kWh. Find the equation for the electricity cost y yen when x kWh are used, and find the amount of electricity used when the cost is 3000 yen.
Answer: y=25x+1000. 3000=25x+1000→25x=2000→x=80 kWh
The basic electricity charge is 1000 yen, and the charge is 25 yen per 1kWh. Find the equation for the electricity cost y yen when x kWh are used, and find the amount of electricity used when the cost is 3000 yen.
Answer: y=25x+1000. 3000=25x+1000→25x=2000→x=80 kWh
Key Points
- In y=ax+b, a is the amount of change for each increase of one unit.
- b is the basic charge or initial value.
- Visualizing the problem with a graph makes its meaning easier to understand.
Practice Problems
- A plan has a monthly basic charge of 500 yen and costs 10 yen for every minute of a call. Express the cost y yen when calling for x minutes, and find how many minutes were used when the cost was 2000 yen.
Answer and Explanation
- Answer: y=10x+500. 2000=10x+500→x=150 minutes.