Direct and Inverse Variation
Variation describes how one quantity changes in relation to another. Direct variation means quantities increase together; inverse variation means one increases as the other decreases.
What You Need to Know
Key Concept Diagram
Direct variation: y = kx, where k is the constant of proportionality
In direct variation, doubling x doubles y; the ratio y/x is always constant
Inverse variation: y = k/x, so xy = k is always constant
In inverse variation, doubling x halves y
Key Vocabulary
Direct variation
A relationship where y = kx; both quantities increase or decrease together
Inverse variation
A relationship where y = k/x; as one quantity increases, the other decreases
Constant of proportionality
The fixed value k in variation equations
Proportion
A relationship where two ratios are equal
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
If y varies directly with x and y = 12 when x = 4, what is y when x = 7?
Question 2
If y varies inversely with x and y = 6 when x = 4, what is y when x = 12?
Question 3
Which equation represents direct variation?
Key Concepts Summary
- ●Direct variation: y = kx, where k is the constant of proportionality
- ●In direct variation, doubling x doubles y; the ratio y/x is always constant
- ●Inverse variation: y = k/x, so xy = k is always constant
- ●In inverse variation, doubling x halves y