To derive the equation of a proportional relationship through the origin using a graph, you generally need two pieces of information: a pair of values (x, y) that correspond to the price and the quantity of footballs.
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Identify Two Points from the Graph: Look at the graph and identify two points through which the line passes. Let's represent these points as \( (x_1, y_1) \) and \( (x_2, y_2) \).
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Calculate the Constant of Proportionality (k): The relationship is of the form \( y = kx \), where \( k \) is the constant of proportionality. You can calculate \( k \) using one of the points. For example, if you choose the point \( (x_1, y_1) \), you can write: \[ k = \frac{y_1}{x_1} \]
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Write the Equation: Substitute the value of \( k \) into the equation \( y = kx \). This gives you the equation of the line that represents the proportional relationship through the origin.
For example, if your points were \( (2, 10) \) and \( (4, 20) \):
- Using the point \( (2, 10) \), \( k = \frac{10}{2} = 5 \).
- The equation would be \( y = 5x \).
If you share specific values from the graph, I can help you derive the exact equation!
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