📚 Topic Summary
In mathematics, two quantities are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other. This constant is called the constant of proportionality. In simpler terms, if one quantity doubles, the other doubles as well. Non-proportional relationships, on the other hand, do not follow this rule; there is no constant ratio between the two quantities. Identifying these relationships is key to solving many real-world problems.
Understanding the difference between proportional and non-proportional relationships is crucial for various applications. Proportional relationships are represented by equations of the form $y = kx$, where $k$ is the constant of proportionality. Non-proportional relationships may take many forms, such as $y = mx + b$, where $b \neq 0$. By recognizing the type of relationship, you can predict how changes in one quantity will affect the other.
🧮 Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. Constant of Proportionality |
A. A relationship where the ratio between two quantities is not constant. |
| 2. Proportional Relationship |
B. The value that relates two quantities in a proportional relationship. |
| 3. Non-Proportional Relationship |
C. The point where a line intersects the y-axis. |
| 4. Y-intercept |
D. A relationship where the ratio between two quantities is constant. |
| 5. Rate of Change |
E. How one quantity changes in relation to another quantity. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided: constant, ratio, proportional, non-proportional, linear.
A __________ relationship exists when there is a __________ __________ between two quantities. This means that one quantity is always a __________ multiple of the other. In contrast, a __________ relationship does not have a __________ rate of change and cannot be expressed in the form $y=kx$. A proportional relationship is also a __________ relationship that passes through the origin $(0,0)$.
🤔 Part C: Critical Thinking
Explain, in your own words, how you can determine whether a table of values represents a proportional relationship. Provide an example to support your explanation.