Interpreting intercepts of linear functions

TL;DR

A cyclist rides at a constant rate and is 10 kilometers from home after 2 hours and 5 kilometers away after 4 hours. The total time it takes to finish the ride and reach home is 6 hours.

Transcript

After several days of camping and long-distance bicycle riding, you decide to ride straight home riding at a constant rate. After 2 hours of riding, you are 10 kilometers from home. And after 4 hours of riding, you are 5 kilometers from home. Once you begin to ride home, in how many hours will you finish your bike ride and arrive at home? This last... Read More

Key Insights

• 💨 The cyclist was 15 kilometers away from home when they started riding back, as shown on the distance-time graph.
• ⌛ The distance decreases by 5 kilometers every 2 hours of riding.
• ⌛ The total time for the ride home is calculated to be 6 hours.
• ⌛ The equation for the distance-time relationship is distance = 15 - (5/2) * time or distance = 15 - (2.5 * time).
• ⌛ The slope of the distance-time graph represents the cyclist's rate, which is -5/2, indicating a decrease of 5 kilometers for every 2 hours of riding.
• 🫥 The graph shows a straight line, suggesting a constant rate of travel throughout the ride.

Questions & Answers

Q: How far was the cyclist from home when they started riding home?

The cyclist was 15 kilometers away from home when they started riding home, as indicated by the initial point on the distance-time graph.

Q: What is the cyclist's rate of travel?

The cyclist's rate of travel can be determined by the slope of the distance-time graph, which is calculated to be -5/2. This means the cyclist is covering 5 kilometers less for every 2 hours of riding.

Q: How can the equation for the distance-time relationship be expressed?

The equation for the distance-time relationship is distance = 15 - (5/2) * time or distance = 15 - (2.5 * time).

Q: Can the cyclist's speed be considered constant throughout the entire ride?

Yes, since the graph shows a straight line, it indicates that the cyclist maintains a constant rate of travel, making it possible to calculate the total time for the ride using the given data.

Summary & Key Takeaways

• After 2 hours of riding, the cyclist is 10 kilometers from home.

• After 4 hours of riding, the cyclist is 5 kilometers from home.

• The cyclist's ride home will take a total of 6 hours.