Fix the mistake: Applications of Linear Functions
Applications of Linear Functions ① Distance-Time Graphs
A graph that represents the relationship between time and distance is called a distance-time graph.
Example ①
Taro began walking from his house to a station 6 km away at 4 km/h, then turned around partway and returned at the same speed. The outward trip was from the house to the station (1.5 hours), and the return trip was from the station to the house (1.5 hours).
(1) Find the equation for the outward trip, where y km is the distance from the house and x hours is the time.
(2) Find the equation for the return trip.
Answer: (1) y=4x（0≦x≦1.5）. (2) At x=1.5, y=6. Since he returns at 4 km/h, y=−4(x−1.5)+6=−4x+12（1.5≦x≦3）.
Taro began walking from his house to a station 6 km away at 4 km/h, then turned around partway and returned at the same speed. The outward trip was from the house to the station (1.5 hours), and the return trip was from the station to the house (1.5 hours).
(1) Find the equation for the outward trip, where y km is the distance from the house and x hours is the time.
(2) Find the equation for the return trip.
Answer: (1) y=4x（0≦x≦1.5）. (2) At x=1.5, y=6. Since he returns at 4 km/h, y=−4(x−1.5)+6=−4x+12（1.5≦x≦3）.
Key Points
- Outward trip: y=(speed)×x
- Return trip: y decreases at the speed from the turning point: y=−(speed)×(x−turning time)＋maximum distance
Practice Problems
- A person walks to a library 8 km from home at 4 km/h (the distance y km after x hours). Find the equation for 0≦x≦2.
Answer and Explanation
- Answer: y=4x.
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