Line Graph DI
Master Line Graphs. Covers Single Line, Double Line Comparison, Cumulative (Running Totals), and Rate-based models.
Model 1: The 'Slope' Concept
- Scenario: Line goes up steeply vs gradually.
- The Rule: Steepness = Growth Rate.
- If the line is almost vertical, the % increase is huge. If it's flat (horizontal), there is NO change (0% growth).
Example:
Q: Value at Year 1 = 100. Year 2 = 150. Year 3 = 160. Which year has higher growth rate?
Solution: Year 2 Growth = 50%. Year 3 Growth = 6.66%. The steeper slope (Y1 to Y2) indicates higher growth.
Model 2: Intersection Points
- Scenario: Two lines (Income and Exp) cross each other.
- The Insight: At the intersection point, Value A = Value B.
- If Income line crosses Expenditure line from below to above, it means the company moved from Loss to Profit.
Example:
Q: At intersection point P, Income = Expenditure. What is the Profit %?
Solution: Profit = Inc - Exp = 0. Profit % = 0/Exp * 100 = 0% (Break First Point).
Model 3: Cumulative Lines (The Trap)
- Scenario: Graph shows "Cumulative Production" up to Year X.
- The Trap: Value at 2020 is 500. Value at 2021 is 800. Student thinks 2021 production is 800.
- The Truth:
Actual 2021 = Cumulative(2021) - Cumulative(2020) = 800 - 500 = 300.
Example:
Q: Cumul Sales: Jan=20, Feb=50. Find Feb Sales.
Solution: Feb Sales = 50 - 20 = 30.
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