Direct Variation Calculator
Calculate direct proportionality relationships using the formula y = k × x
Direct Variation Calculator
The input or independent variable
The output or dependent variable
The proportionality constant
Direct Variation Results
Direct Variation Graph
Enter values to see graph
y = kx
Input Validation
Example Problems
Example 1: Ohm's Law
Problem: If voltage (V) varies directly with current (I), and V = 12V when I = 2A, what is V when I = 3A?
Given: V = 12V, I = 2A
Find constant: k = V ÷ I = 12 ÷ 2 = 6Ω (resistance)
Calculate: V = k × I = 6 × 3 = 18V
Example 2: Distance and Speed
Problem: Distance varies directly with time at constant speed. If you travel 120 miles in 2 hours, how far in 5 hours?
Given: d = 120 miles, t = 2 hours
Find speed: k = d ÷ t = 120 ÷ 2 = 60 mph
Calculate: d = k × t = 60 × 5 = 300 miles
Direct Variation Formula
or y ∝ x
Dependent Variable
Output that depends on x
Independent Variable
Input that can be controlled
Constant of Variation
Proportionality constant
Properties of Direct Variation
Graph is a straight line through origin
Slope equals constant k
When x increases, y increases proportionally
Ratio y/x remains constant
If x = 0, then y = 0
Understanding Direct Variation
What is Direct Variation?
Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. When x increases, y increases proportionally, and when x decreases, y decreases proportionally.
Key Characteristics
- •The graph passes through the origin (0,0)
- •The relationship forms a straight line
- •The constant k represents the slope
- •Doubling x doubles y
Real-World Examples
Physics - Ohm's Law
Voltage varies directly with current: V = I × R
Motion - Distance
At constant speed: Distance = Speed × Time
Economics - Cost
Total cost varies with quantity: Cost = Price × Quantity
Geometry - Circumference
Circumference varies with diameter: C = π × d
How to Recognize Direct Variation
Check the Ratio
If y₁/x₁ = y₂/x₂ = y₃/x₃, then it's direct variation
Plot the Points
If points form a straight line through origin, it's direct variation
Test the Formula
If y = kx where k is constant, it's direct variation