Finding Direct Variation
Identify direct variation relationships in Grade 10 algebra where y=kx, calculate the constant of variation k from a table or graph, and write the direct variation equation.
Key Concepts
New Concept When a problem states that $A$ varies directly as $B$, the equation $A = kB$ is implied. This relationship is called direct variation.
Why it matters Direct variation is your first tool for translating real world patterns into the language of algebra. Mastering this simple linear relationship is the foundation for modeling everything from chemical reactions to economic trends.
What’s next Next, you’ll translate word problems into the equation $A=kB$, find the constant of variation, and solve for unknown values.
Common Questions
How do you identify direct variation from a table of values?
Compute the ratio y/x for each pair. If the ratio is constant, the data shows direct variation and k=y/x is the constant of variation.
Write the direct variation equation if y=15 when x=3.
k=y/x=15/3=5. Equation: y=5x.
How does the graph of a direct variation equation look?
It is a straight line through the origin (0,0) with slope k. Any direct variation y=kx passes through the origin, distinguishing it from general linear equations with a non-zero y-intercept.