Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Rational Equations
3:18 minutes
Problem 54b
Textbook Question
Textbook QuestionAnswer each question. What happens to y if y varies directly as x, and x is halved?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Direct Variation
Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. If y varies directly as x, it can be expressed as y = kx, where k is a non-zero constant. This means that as x changes, y changes in a proportional manner.
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Proportional Relationships
In a proportional relationship, the ratio of the two variables remains constant. For example, if y varies directly as x, then the ratio y/x = k remains the same regardless of the values of x and y. This concept is crucial for understanding how changes in one variable affect the other in direct variation.
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Effect of Halving x
When x is halved in a direct variation scenario, the value of y will also be halved. This is because if x is reduced to x/2, substituting this into the direct variation equation y = kx results in y = k(x/2) = (k/2)(x), demonstrating that y is directly proportional to x and will change accordingly.
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