To quickly check for proportional relationships using a graph, you can follow these steps:
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Understand Proportional Relationships: A relationship is proportional if it can be expressed in the form \( y = kx \), where \( k \) is a constant. This means that the ratio \( \frac{y}{x} \) is constant.
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Plot the Points: If you have a set of data points, plot them on a coordinate grid.
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Check for a Straight Line Through the Origin: Draw a line through the plotted points. If the line passes through the origin (0,0) and is straight, the relationship is likely proportional.
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Check the Ratios: If you have specific points \( (x_1, y_1) \) and \( (x_2, y_2) \) on the graph, check their ratios:
- Calculate \( \frac{y_1}{x_1} \) and \( \frac{y_2}{x_2} \).
- If these ratios are equal, the points represent a proportional relationship.
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Identify Constant Variation: If the graph shows a constant slope and passes through the origin, the relationship is proportional.
Quick Check Example:
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Data Points: (1, 2), (2, 4), (3, 6)
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Graph: Plot these points.
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Check for Proportionality:
- Ratios: \( \frac{2}{1} = 2 \), \( \frac{4}{2} = 2 \), \( \frac{6}{3} = 2 \) (all equal).
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Graph Characteristics: Confirm the graph is a straight line through (0,0).
If both conditions are satisfied, the relationship is proportional. If the line does not pass through the origin or is not straight, the relationship is not proportional.