1. What is Direct and Inverse Variation?

Direct variation describes a relationship where y changes directly with x (y = kx), while inverse variation describes a relationship where y changes inversely with x (y = k/x). In both cases, k is the constant of variation that defines the specific relationship.

2. How Does the Calculator Work?

The calculator uses the variation equations:

Steps:

1. Determine the constant of variation (k) using known x and y values
2. Apply the constant to calculate new y values for given x values

3. Practical Applications

Direct Variation Examples: Distance vs. time at constant speed, cost vs. number of items
Inverse Variation Examples: Brightness vs. distance from light source, time vs. work rate

4. Using the Calculator

Instructions: Select variation type, enter one known (x,y) pair, and the new x value to find the corresponding y value.

5. Frequently Asked Questions (FAQ)

Q1: How do I know if a relationship is direct or inverse?
A: In direct variation, y increases as x increases. In inverse variation, y decreases as x increases.

Q2: Can x be zero in these equations?
A: No, x cannot be zero in inverse variation (division by zero). In direct variation, x=0 gives y=0.

Q3: What units does the constant k have?
A: The units of k depend on the units of x and y. For direct variation: k = y/x. For inverse variation: k = y×x.

Q4: Can this calculator handle non-linear variations?
A: No, this calculator only handles simple direct (y∝x) and inverse (y∝1/x) relationships.

Q5: How accurate are the results?
A: Results are mathematically exact for ideal direct/inverse variation relationships.