Direct Variation

Direct variation: what to do

In a direct variation, one variable is proportional to another. The relationship has the form

[ y = kx ]

where (k) is the constant of variation. Your task is usually to find (k), write the equation, or use it to find a missing value.

Step-by-step method

1. Identify the known pair. Use the given values of (x) and (y).
2. Find the constant of variation. Substitute into (y = kx) and solve for (k): [ k = \frac{y}{x} ] as long as (x \neq 0).
3. Write the direct variation equation. Replace (k) in (y = kx).
4. Solve for the missing value. Substitute the new (x) or (y) value and simplify.

Check your answer

Make sure the ratio (\frac{y}{x}) stays the same for every pair in a direct variation. Also check that your final answer is simplified and has the correct sign.

Common reminder

If the problem gives a table, ordered pairs, or a word situation, use the same method: compare the values, find (k), then use the equation to answer the question.