Mathematics
Grade 9
15 min
Identify direct variation and inverse variation
Identify direct variation and inverse variation
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define direct and inverse variation.
Identify the constant of variation, k, in an equation or table.
Distinguish between direct and inverse variation when given an algebraic equation.
Determine if a table of values represents direct variation, inverse variation, or neither.
Classify a real-world scenario as an example of direct or inverse variation.
Differentiate between a direct variation relationship and a general linear relationship.
Ever notice that the more hours you work, the more money you earn? š° Or that the faster you drive, the less time it takes to get to your destination? š
These predictable relationships are called variations. In this tutorial, you will learn how to identify the two most common types: direct variation and inverse variation...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariationA relationship between two variables where a change in one variable causes a predictable, corresponding change in the other.The relationship between the number of tickets you buy for a concert and the total cost.
Direct VariationA relationship between two variables, x and y, where as one increases, the other increases by a constant factor. Similarly, as one decreases, the other decreases by the same constant factor.If you earn $15 per hour, your total earnings (y) vary directly with the number of hours you work (x). More hours means more pay.
Inverse VariationA relationship between two variables, x and y, where as one variable increases, the other variable decreases by a constant factor.If you have a 24-slice pizza, the number of slices each person gets (y)...
3
Core Formulas
Direct Variation Formula
y = kx or k = y/x
Use this to identify direct variation. The variable y is a constant multiple of x. The ratio of y to x is always equal to the constant of variation, k. The graph of a direct variation is a line that passes through the origin (0,0).
Inverse Variation Formula
y = k/x or xy = k
Use this to identify inverse variation. The variable y is found by dividing the constant k by x. The product of x and y is always equal to the constant of variation, k. The graph of an inverse variation is a hyperbola, not a straight line.
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
The equation for the area of a square is A = sĀ², where A is the area and s is the side length. Why is this relationship NOT a direct variation?
A.Because the area increases as the side length increases.
B.Because the equation does not have a y-intercept.
C.Because the variable 's' is raised to the power of 2.
D.Because the constant of variation is 1.
Challenging
A scientist collects the following data. What is the relationship between x and y, and what is the constant of variation k?
x | 0.2 | 0.8 | 4
--|-----|-----|---
y | 120 | 30 | 6
A.Direct variation, k = 600
B.Inverse variation, k = 24
C.Direct variation, k = 24
D.Inverse variation, k = 600
Challenging
A relationship between two variables is graphed on a coordinate plane. The graph is a straight line that passes through the points (2, 6) and the origin (0,0). What kind of relationship must this be?
A.An inverse variation.
B.direct variation.
C.linear relationship, but not a direct variation.
D.Neither a linear nor a variation relationship.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free