Sure! Here are the key points to remember about graphs of proportional relationships for a quick check:
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Definition: A proportional relationship is one in which two quantities maintain a constant ratio. When one quantity changes, the other changes in such a way that the fraction (ratio) between them remains the same.
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Equation: Usually represented in the form \( y = kx \), where \( k \) is the constant of proportionality.
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Graph Characteristics:
- Shape: The graph of a proportional relationship is a straight line.
- Origin: The line passes through the origin (0, 0).
- Slope: The slope of the line is equal to the constant of proportionality (k).
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Examples:
- If \( k = 2 \), the relationship can be represented as \( y = 2x \). The graph will be a straight line passing through (0,0) and (1,2), (2,4), etc.
- If \( k = 0.5 \), the relationship can be represented as \( y = 0.5x \). The line will be less steep and still pass through the origin.
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Non-examples:
- Any graph that does not pass through the origin.
- Curved lines or any line that does not maintain a constant slope.
By keeping these points in mind, you can quickly identify and analyze graphs of proportional relationships! If you have specific graphs or relationships in mind, feel free to share for further analysis!