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Line Graph DI

Master Line Graphs. Covers Single Line, Double Line Comparison, Cumulative (Running Totals), and Rate-based models.

Model 1: The 'Slope' Concept

      <ul class='list-disc pl-6'>
        <li><strong>Scenario:</strong> Line goes up steeply vs gradually.</li>
        <li><strong>The Rule:</strong> <span class="text-primary-600 font-bold">Steepness = Growth Rate</span>.</li>
        <li>If the line is almost vertical, the % increase is huge. If it's flat (horizontal), there is NO change (0% growth).</li>
      </ul>

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

      <ul class='list-disc pl-6'>
        <li><strong>Scenario:</strong> Two lines (Income and Exp) cross each other.</li>
        <li><strong>The Insight:</strong> At the intersection point, Value A = Value B.</li>
        <li>If Income line crosses Expenditure line from below to above, it means the company moved from <span class="text-red-600 font-bold">Loss</span> to <span class="text-primary-600 font-bold">Profit</span>.</li>
      </ul>

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)

      <ul class='list-disc pl-6'>
        <li><strong>Scenario:</strong> Graph shows "Cumulative Production" up to Year X.</li>
        <li><strong>The Trap:</strong> Value at 2020 is 500. Value at 2021 is 800. Student thinks 2021 production is 800.</li>
        <li><strong>The Truth:</strong> <br>Actual 2021 = Cumulative(2021) - Cumulative(2020) = 800 - 500 = 300.</li>
      </ul>

Example:

Q: Cumul Sales: Jan=20, Feb=50. Find Feb Sales.

Solution: Feb Sales = 50 - 20 = 30.