Graph Analysis: Interpreting a Sprinter's Speed-Time Relationship

Graph Interpretation with Decreasing Linear Functions

Select the graph that best demonstrates the following trend:

A sprinter who runs at a certain speed (Y) and gradually gets tired over time (X).

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Step-by-step written solution

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1

Understand the problem

Select the graph that best demonstrates the following trend:

A sprinter who runs at a certain speed (Y) and gradually gets tired over time (X).

2

Step-by-step solution

The runner starts at a high speed and as time passes, he loses his strength and runs slower.

In other words, the graph will be descending, and therefore answer C is correct.

3

Final Answer

WeatherSpeed 000

Key Points to Remember

Essential concepts to master this topic
  • Trend Analysis: Decreasing functions show negative relationships between variables
  • Technique: High start, low end = downward slope from left to right
  • Check: Verify direction matches real-world scenario: tired sprinter runs slower ✓

Common Mistakes

Avoid these frequent errors
  • Confusing increasing and decreasing graph directions
    Don't choose upward-sloping graphs for decreasing relationships = opposite trend! This shows the sprinter getting faster over time, which contradicts getting tired. Always match graph direction to the described relationship: tired = slower = downward slope.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

How do I tell if a graph is increasing or decreasing?

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Look at the graph from left to right. If it goes up, it's increasing. If it goes down, it's decreasing. Think of it like reading a book!

Why does 'getting tired' mean the graph goes down?

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When someone gets tired, their performance decreases. Since speed is on the y-axis, lower performance means lower on the graph, creating a downward trend.

What if the graph shows ups and downs?

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A wavy or curved graph might show temporary changes, but for a sprinter gradually getting tired, we expect a steady downward trend over time.

Does the steepness of the line matter?

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The steepness shows how quickly the sprinter gets tired. A steeper downward line means getting tired faster, but any downward slope shows the right trend.

Can the speed ever go to zero?

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In theory, yes! If the sprinter gets completely exhausted, their speed could approach zero. The graph would show this as the line getting very close to the x-axis.

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