Direct Variation Behavior
Direct variation behavior is a Grade 6 math concept in Big Ideas Math Advanced 1, Chapter 14: Ratios and Proportions. Two quantities show direct variation when their ratio is constant — as one quantity increases, the other increases proportionally. The relationship is expressed as y = kx, where k is the constant of variation (unit rate).
Key Concepts
Suppose $y$ and $x$ are related by the equation $y = kx$ (direct variation).
If $x$ is multiplied by a factor $b$, then $y$ is also multiplied by the same factor $b$.
Common Questions
What is direct variation in Grade 6 math?
Direct variation describes a relationship where two quantities change proportionally together. If y varies directly with x, then y = kx for some constant k. When x doubles, y doubles; when x triples, y triples.
How do you identify direct variation in a table?
In a table showing direct variation, every y/x ratio must equal the same constant k. If dividing each y-value by its corresponding x-value gives the same result, the relationship is direct variation.
What is the constant of variation?
The constant of variation k is the ratio y/x in a direct variation relationship. It is the unit rate — how much y changes for each 1-unit increase in x. On a graph, it equals the slope of the line.
Where is direct variation taught in Big Ideas Math Advanced 1?
Direct variation behavior is covered in Chapter 14: Ratios and Proportions of Big Ideas Math Advanced 1, the Grade 6 math textbook.
How does direct variation appear on a graph?
A direct variation relationship graphs as a straight line that passes through the origin (0, 0). The steepness of the line equals the constant of variation k.