# Direct Variation Definition

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Direct variation definition is that two variables are related in such a way that when one variable changes then the other variable changes in proportion. In simple words, direct variation shows the relationship between two variables which is expressed by an equation. Direct variation is a special case of linear equation. If A is directly proportional to B, then the equation is A= k* B where k is a constant.

Problem 1: If y varies directly as x, and y =18 when x = 12, find k and write equation.

Solution: Given: y varies directly as x that means y is directly proportional to x

=> So, the equation is y = k x

=> The values of x =12 when y =18

=> Plug in the values and solve for k

=> The equation is y = k x

=> 18 = k * 12

=> Then k = 18 /12 = 3/2

=> Thus, the value of k = 3/2

=> Now, go back to equation y= k x and substitute k = 3/2

=> The required equation is y = (3/2) x

Problem 2: In a factory, the profit, P, varies directly with the inventory, I.  If P = 200 when I = 40. Find P when I = 50.

Solution: Since P varies directly with inventory l

=> The equation is P = k*l

=> We use given set of data to get value of constant k.

=> If p=200 when l = 40 then 200 = k * 40

=> K = 200/40 = 5

=> Now, Find P when l = 50

=> P = k*l

=> P = 5 * 50 = 250