# Direct Variation Example

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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.