Green Bridge Learning Resource For Direct And Inverse Variation

Overview

Some quantities rise and fall together: drive twice as long at a steady speed and you cover twice the distance. Others move in opposite directions: double the number of workers and a job takes half the time. These two patterns, direct and inverse variation, capture an enormous range of everyday relationships in a single, simple equation.

In this lesson you will write direct and inverse variation algebraically, find the constant of variation from given information, and use the resulting equation to find unknown quantities. The key is the constant: once you have it, the whole relationship is fixed.

Lesson Evaluation

Congratulations on completing the lesson on Direct And Inverse Variation. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

If y varies directly as x and y = 12 when x = 3, what is the constant of variation? A. 3 B. 4 C. 9 D. 36 Answer: B
If y = 4x, what is y when x = 5? A. 9 B. 16 C. 20 D. 45 Answer: C
If y varies inversely as x and y = 6 when x = 2, the constant is: A. 3 B. 8 C. 12 D. 4 Answer: C
If y = 12/x, what is y when x = 4? A. 3 B. 4 C. 8 D. 48 Answer: A
Which relationship is inverse variation? A. y = kx B. y = k + x C. y = k/x D. y = x/k Answer: C