A proportional pattern relates two quantities through a constant multiplicative relationship: equivalent ratios or unit rates remain equal, and its table or graph pairs zero with zero and forms a line through the origin. Non-proportional patterns may have a changing ratio, a fixed starting amount, or an additive change without a constant ratio; distinguishing these in verbal descriptions, tables, graphs, and simple equations prepares learners for proportional reasoning and algebra without requiring formal slope calculations or generalized proofs.
A pattern is proportional when one quantity is always the same multiple of the other. You can check this by:
Example: A taxi charges a starting fee of 3$2$ for each mile.
| Miles, | Cost, |
|---|---|
| 3$ | |
| 5$ | |
| 7$ | |
| 9$ |
First, check what happens when the number of miles is . The cost is 3$0$. This means there is a fixed starting fee.
Next, compare the ratios for positive numbers of miles:
The ratios are not equal, so there is no constant unit rate from miles to total cost.
Therefore, this is a non-proportional pattern. The cost increases by 2$300$.
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