For a graph to represent a proportional relationship, it must satisfy two key conditions:
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Passes through the Origin: The graph must pass through the point (0, 0). This indicates that when the independent variable (often represented on the x-axis) is zero, the dependent variable (represented on the y-axis) is also zero. In a proportional relationship, there is no constant term that shifts the graph away from the origin.
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Constant Ratio: The graph must show a straight line that has a constant slope, which means that the ratio of the dependent variable to the independent variable remains constant. This is often expressed as \( y = kx \), where \( k \) is the constant of proportionality. For any two points on the line, the ratio \( \frac{y}{x} \) will always equal \( k \), indicating that as one variable changes, the other changes at a consistent rate.
If both of these conditions are satisfied, the graph represents a proportional relationship.
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