A proportional relationship exists between two variables when their ratio is constant. This means that as one variable increases, the other increases at a consistent rate, and their relationship can be represented by the equation $y = kx$, where $k$ is the constant of proportionality. Identifying proportional relationships is crucial in various real-world applications, such as scaling recipes, calculating distances on maps, and determining unit prices.
In simpler terms, if you double one quantity, the other quantity doubles as well. If you halve one quantity, the other is halved too. The constant of proportionality, $k$, tells us exactly how the two quantities are related. This quiz will help you practice identifying and working with proportional relationships!
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Constant of Proportionality | A. A relationship where the ratio between two variables is constant. |
| 2. Proportional Relationship | B. The value that relates two variables in a proportional relationship ($k$ in $y=kx$). |
| 3. Rate | C. A comparison of two quantities with different units. |
| 4. Unit Rate | D. A rate where the second quantity is one unit. |
| 5. Ratio | E. A comparison of two quantities. |
Complete the following paragraph using the words: proportional, constant, ratio, equation, and variables.
Two __________ are in a __________ relationship if their __________ is always the same. This __________ value is called the __________ of proportionality. We can represent this relationship with an __________ like $y = kx$, where $k$ is the constant of proportionality.
Explain, in your own words, how you can determine if a table of values represents a proportional relationship. Provide an example.
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