Identifying, Writing, and Graphing Inverse Variation
Identify, write, and graph inverse variation in Grade 9 algebra. Recognize y=k/x, calculate the constant of variation k, and graph the hyperbolic relationship on a coordinate plane.
Key Concepts
New Concept Inverse variation is a relationship between two variables whose product is a constant. The equation is $xy = k$ or $y = \frac{k}{x}$. What’s next Next, you’ll use this definition to identify inverse variations, find missing values in a relationship, and graph the resulting curves.
Common Questions
What is inverse variation and how is it written?
Inverse variation describes one variable increasing as the other decreases proportionally. Written y = k/x or xy = k, where k is the constant of variation.
How do you find the constant of variation k in inverse variation?
Multiply any known x and y pair: k = xy. Once you have k, use y = k/x to find other values. The product xy always equals k for all points in an inverse variation.
What does the graph of an inverse variation look like?
The graph is a hyperbola with two branches. For positive k, branches are in quadrants I and III. The axes are asymptotes — the graph approaches but never touches them.