Solving Inverse Variation Problems
Identify inverse variation relationships in Grade 10 algebra where y = k/x, find the constant of variation k from data points, and distinguish inverse from direct variation.
Key Concepts
New Concept If the product of two variables is a constant, then the equation is an inverse variation. $$xy = k \text{ or } y = \frac{k}{x}$$.
Why it matters Algebra is the language of relationships, and inverse variation describes a fundamental pattern where one quantity shrinks as another grows. Mastering this concept allows you to model complex real world systems, from gravitational forces to economic principles of supply and demand.
What’s next Next, you’ll learn to identify this relationship in data tables and use it to solve for unknown values.
Common Questions
What is the equation for inverse variation?
y = k/x, where k is the constant of variation. As x increases, y decreases proportionally. The product xy = k is always constant.
How do you find the constant of variation k from a table?
Compute xy for each data pair. If all products are equal, the data shows inverse variation and k equals that product. For example, if x=2,y=6, then k=12.
How do you distinguish inverse variation from direct variation?
Direct variation: y = kx (ratio y/x is constant). Inverse variation: y = k/x (product xy is constant). Plot the data: direct variation is linear through origin; inverse variation is a hyperbola.