Direct Variation Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easy\(y\) varies directly with \(x\), and \(y = 18\) when \(x = 3\). Find the constant \(k\) and write the direct variation equation.
Solution
- 1 Direct variation: \(y = kx\).
- 2 Find \(k\): \(k = y/x = 18/3 = 6\).
- 3 Equation: \(y = 6x\).
- 4 Check: when \(x=3\), \(y = 6 \times 3 = 18\) ✓
Answer
\(k = 6\); \(y = 6x\)
In direct variation \(y = kx\), \(k\) is found by dividing \(y\) by \(x\). Here \(k = 18/3 = 6\).
About Direct Variation
A proportional relationship that always passes through the origin — when one quantity doubles, so does the other.
Learn more about Direct Variation →More Direct Variation Examples
Example 2 medium
The cost of fabric varies directly with length. 5 meters costs $35. How much do 8 meters cost? Set u
Example 3 easyIf (y = kx) and (y = 24) when (x = 4), find (y) when (x = 7).
Example 4 mediumA machine produces 150 units in 5 hours. Assuming direct variation, how many units in 9 hours?