To derive the equation of a proportional relationship from a graph, we typically need to identify two key components from the graph: a specific point (usually the origin) and the slope of the line, which represents the rate of change in price with respect to another variable (often quantity).
Here's a step-by-step guide on how one might derive the equation:
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Identify Points on the Graph: Start by identifying the points on the graph. The origin (0,0) is often where the relationship starts, especially in a proportional relationship (assuming you are considering the price of footballs when no footballs are being sold, the price is $0).
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Determine the Slope: The slope (m) can be calculated if you know two points on the line. The slope is computed using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.
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Write the Proportional Relationship: Proportional relationships can be expressed in the form:
\[ y = mx \]
where \(y\) is the dependent variable (price, in this case), \(x\) is the independent variable (number of footballs), and \(m\) is the slope you calculated.
If you can provide specific values or points from the graph, I can help you derive the exact equation!