📚 Topic Summary
Proportional relationships are all about constant ratios. A table represents a proportional relationship if the ratio between the $y$-value and the $x$-value is the same for every pair of values in the table. This constant ratio is called the constant of proportionality. If the ratio changes, then the relationship is not proportional. Think of it like a recipe – you need to keep the ingredients in the same proportion for it to turn out right! You can determine proportionality by calculating $k = \frac{y}{x}$ for each pair of values.
Let's work through some practice problems to solidify your understanding! This worksheet contains a vocabulary section, some fill-in-the-blanks, and a critical thinking question.
🧠 Part A: Vocabulary
Match the following 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 constant ratio between two variables in a proportional relationship. |
| 3. Ratio |
C. A comparison of two quantities by division. |
| 4. Table |
D. An arrangement of data in rows and columns. |
| 5. Variable |
E. A symbol that represents a quantity that can change. |
(Match the term number with the definition letter, e.g., 1-B)
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided (Constant, Proportional, Ratio, Table, Variables):
A ___________ relationship exists when the ___________ between two ___________ remains the same. This constant value is called the ___________. You can display a proportional relationship in a ___________.
🤔 Part C: Critical Thinking
Explain, in your own words, how you can determine if a table represents a proportional relationship. Provide an example.