Identifying, Writing, and Graphing Inverse Variation Practice — Grade 9 math

Lesson 64: Identifying, Writing, and Graphing Inverse Variation — Practice Questions

1. If y varies inversely with x, and y = 7 when x = 6, what is the constant of variation, k? ___
2. The variables $a$ and $b$ vary inversely. If $a=5$ when $b=10$, which equation correctly describes this relationship?
- A. $a = 2b$
- B. $a = \frac{2}{b}$
- C. $a = \frac{50}{b}$
- D. $a = 50b$
3. Given that y varies inversely with x, and y = 4 when x = 15. What is the value of y when x = 10? ___
4. The relationship between $y$ and $x$ is an inverse variation with a constant of variation $k=36$. Which of the following ordered pairs $(x, y)$ could exist in this relationship?
- A. (4, 8)
- B. (3, 12)
- C. (6, 5)
- D. (2, 16)
5. The time it takes to set up for an event varies inversely with the number of workers. If it takes 2 workers 8 hours, how many hours would it take 4 workers? ___
6. Which of the following equations shows that $y$ varies inversely with $x$?
- A. $y = x + 8$
- B. $y = \frac{x}{8}$
- C. $xy = 8$
- D. $y = 8x$
7. The variables $x$ and $y$ vary inversely. If $x=5$ when $y=6$, what is the value of $y$ when $x=10$? The value is ___.
8. If it takes 4 chefs 5 hours to prepare a banquet, how long would it take 10 chefs to prepare the same banquet? It would take ___ hours.
9. The time it takes to drive a certain distance varies inversely with the speed. If you double your speed, what happens to the travel time?
- A. It is doubled.
- B. It is halved.
- C. It stays the same.
- D. It is quartered.
10. The variables $p$ and $q$ vary inversely, and their product is 48. If $p=12$, what is the value of $q$? The value of $q$ is ___.