📚 Topic Summary
Inverse variation describes a relationship where one quantity increases as another quantity decreases. Mathematically, this is represented as $y = \frac{k}{x}$, where $y$ and $x$ are the variables, and $k$ is the constant of variation. Understanding inverse variation is essential in many real-world applications, from physics to economics.
In simpler terms, imagine you're dividing a pizza. The more people you share it with, the smaller each slice becomes. That's inverse variation in action!🍕
🧠 Part A: Vocabulary
Match the terms with their correct definitions:
- Constant of Variation
- Inverse Variation
- Variable
- Equation
- Proportion
- A mathematical statement that two expressions are equal.
- A symbol representing a quantity that can change.
- A relationship where one quantity increases as another decreases.
- The constant value ($k$) in an inverse variation equation ($y = \frac{k}{x}$).
- A statement that two ratios are equal.
Matching Answers:
1-D, 2-C, 3-B, 4-A, 5-E
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
In ________ variation, as one quantity ________, the other quantity decreases. The equation representing this relationship is $y = \frac{k}{x}$, where $k$ is the ________ of variation. This means that the product of $x$ and $y$ is always ________. Therefore, if $x$ doubles, $y$ will be ________.
Answer:
In inverse variation, as one quantity increases, the other quantity decreases. The equation representing this relationship is $y = \frac{k}{x}$, where $k$ is the constant of variation. This means that the product of $x$ and $y$ is always constant. Therefore, if $x$ doubles, $y$ will be halved.
🤔 Part C: Critical Thinking
Describe a real-world scenario, different from the pizza example, that demonstrates inverse variation. Explain how the quantities are related.
Example Answer:
Consider the relationship between the speed of a car and the time it takes to travel a fixed distance. If the distance is constant (e.g., 100 miles), then as the speed of the car increases, the time taken to complete the journey decreases. For instance, if you double the speed, you halve the time required to travel the same distance. This perfectly exemplifies inverse variation.