Q1
What is direct variation?
Ay = kx, quantities increase together
By = k/x, one increases as other decreases
CNo relationship exists
DQuantities are always equal
ICSEClass 8 (ICSE)MathematicsCh 10 · Topic 1
Direct and Inverse Variation
Direct variation means two quantities increase or decrease together proportionally, while inverse variation means one increases as the other
Core concept
In direct variation, y = kx (where k is a constant), meaning if x doubles, y also doubles, like distance and time at constant speed.
How it works
In inverse variation, y = k/x, meaning if x doubles, y halves, like speed and time for a fixed distance.
Why it matters
We identify the type of variation by observing how quantities change together in a given problem or dataset.
Key detail
Understanding variation helps us model and solve real-world problems involving proportional relationships between quantities.
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• Direct variation: y = kx.
• If x doubles, y doubles too.
• Example: distance and time at constant speed.
• Inverse variation: y = k/x.
• If x doubles, y halves.
• Example: speed and time for fixed distance.
• We identify variation type from how quantities change.
• Variation helps model real-world proportional relationships.