Direct variation formula is used when two things are directly proportional. This formula shows relation of two variables such that the value of variable increases or decreases as the other variable increases or decreases. That means two variables are proportional to each other. Means, it is an expression that shows relation between variables whose ratio is a constant.
Direct variation formula is y = k x, that is y is directly proportional to each other.
Problem 1: The earnings of Liana vary directly as the number of hours she worked. If 11 hours represents $330.00, determine the earnings of working 15 hours.
Solution: Given Earnings (y) vary directly as the number of hours she worked. So y = k x
=> Put the values we know (y=330 and x=11):
=> 330 = k * 11 by dividing both sides by 11
=> 330/11 = k × * 11/11
=> 30 = k × 1
=> k = 30
=> If number of working hours = 15 then
=> y = k x = 30 * 15 = 450
=> She earns $450 for 15 hours.
Problem 2: If P is directly proportional to Q, and P = 12 when Q = 4, what is the value of P, when Q = 12?
Solution: Given P is directly proportional to Q, so P = k Q
=> Find value of constant k
=> We know P = 12 and Q= 4,
=> So the equation is 12 = k * 4
=> Divide by 4 on both sides,
=> Thus, value of k = 3.
=> When Q = 12 then P = k Q = 3 * 12 = 36
=> Thus the value of P = 36 when Q =12.