Direct Variation

Direct variation occurs when two variables grow larger or smaller together at a consistent rate. The equation that represents this relationship is y = kx, where k is called the constant of variation and is never equal to zero.

To solve direct variation problems, you need to find the constant k using given values, then substitute this constant into the equation. For example, if x and y vary directly and y = 10 when x = 2, you can find k by solving 10 = k(2), which gives k = 5. The equation becomes y = 5x, allowing you to find y for any value of x.

Let's look at another example: if y = 27 when x = 3, then 27 = k(3), so k = 9 and the equation is y = 9x. When x = 6, you can calculate that y = 54. Similarly, if y = 2 when x = 10, then k = 1/5 and the equation becomes y = $1/5$x.

💡 Remember that direct variation always creates a straight line passing through the origin (0,0) on a graph. The constant k represents the slope of this line.