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Last Updated Sep 13, 2025

Touching the axes Simplified Revision Notes

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Touching the axes

1. Understanding Axes Intersections

A graph may touch the axes, indicating a specific meaning:

  • Touching the vertical axis (y-axis):
    • The horizontal value (x) is zero.
    • Example: At x = 0, the initial value of the dependent variable is given.
  • Touching the horizontal axis (x-axis):
    • The vertical value (y) is zero.
    • Example: At y = 0, the dependent variable has reached zero.

Tip: Identifying where the graph touches an axis helps understand starting points and trends.

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2. Worked Example

Scenario:

Tumbo empties a 500 ml water bottle at a constant rate.

Graph Interpretation:

  • The graph shows a steady decrease in water volume over time.
  • At time = 0 minutes, the bottle is full (500 ml).
  • At time = 5 minutes, the bottle is empty (0 ml).

Key Observations:

  • The graph starts at (0, 500) → meaning at 0 minutes, the bottle is full.
  • The graph touches the x-axis at (5,0) → meaning at 5 minutes, the bottle is empty.
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3. Key Takeaways

  • Touching the y-axis: Shows the starting value of the dependent variable.
  • Touching the x-axis: Shows when the dependent variable reaches zero.
  • Used in real-life scenarios such as water levels, speed reduction, and financial balance changes.
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