🍎 Topic Summary
A proportional relationship exists between two quantities when their ratio is constant. In simpler terms, as one quantity increases, the other increases at a consistent rate. We can represent these relationships in tables where the ratio between corresponding values remains the same. These tables help us easily identify and work with proportional relationships.
For example, if you buy apples at a price of $2 per apple, the total cost is proportional to the number of apples you buy. A table can show this: 1 apple costs $2, 2 apples cost $4, 3 apples cost $6, and so on. The ratio \(\frac{\text{cost}}{\text{number of apples}}\) is always 2.
🔤 Part A: Vocabulary
Match the term with its definition:
- Term: Constant of Proportionality
- Term: Proportional Relationship
- Term: Ratio
- Term: Table
- Term: Unit Rate
- Definition: A comparison of two quantities by division.
- Definition: A relationship where two quantities increase or decrease at the same rate.
- Definition: A value that describes the proportional relationship between two variables, often denoted as k.
- Definition: A display of information in rows and columns.
- Definition: The amount for a single item or unit.
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: proportional, constant, ratio, table, unit rate.
A ___________ relationship exists when the ___________ between two quantities is ___________. We can organize these values in a ___________. The ___________ is especially useful for finding the value of one item.
🤔 Part C: Critical Thinking
Explain, in your own words, how a table can help you determine if a relationship is proportional. Provide an example.