Direct variation example involves problems with one variable that is directly proportional to other variable. The relationship between two variables in direct variation is that one variable is a constant multiplication of another. In simple words, if one variable is product of other variable and a constant, then two variables are said to be in direct variation. For example, if y is directly proportional to x and k is a non zero constant then y = k * x
Problem 1: y is directly proportional to x, and when x=6 then y=30. What is the constant of proportionality?
Solution: Given: y is directly proportional to x. So y = k x
=> Put the values we know (y=30 and x=6):
=> 30 = k * 6 by dividing both sides by 6
=> 30/6 = k × * 6/6
=> 5 = k × 1
=> k = 5
=> The constant of proportionality is 5: So the equation is y = 5 x
Problem 2: If y varies directly as x, and y = 24 when x = 16, find y when x = 7
Solution: Given: y varies directly as x, so y = k x
=> Using the given values find value of constant k
=> We know y = 24 and x= 4,
=> So the equation is 24 = k * 4
=> Divide by 4 on both sides,
=> Thus, value of k = 6.
=> When x = 7 then y = k x = 6 * 7 = 42
=> Thus the value of y = 42 when x =7.