Directly proportional means two variables that increase or decrease at the same time. If two variables are proportional if a change in one variable is accompanied by a change in another variable. We can also say that if two quantities are said to be in proportional then one quantity is a constant multiple of other quantity. Two quantities a and b are said to be directly proportional, if the relationship can be written as a = k b where k is a proportionality constant.
Problem 1: The term A is directly proportional to x. And when A is 12, x is 4. Find the value of A when x is 10.
Solution: Since A is directly proportional to x.
=> This can be written as A = k x, where k is proportionality constant.
=> Given When A is12, x is 4
=> Find out constant from the known values A = k x
=> 12 = k * 4
=> By dividing 4 on both sides, we get k = 3
=> When x is 10 then A = k x = 3 * 10 = 30
=> Therefore, when x is 10 the value of A is 30.
Problem 2: A term Y is directly proportional to the square of x. And when Y is 24, x is 2. Find the value of Y when x is 5.
Solution: Given Y is directly proportional to x^2.
=> So, Y = k x^2
=> Substitute the given values (Y= 24, x = 2)
=> Y = k x^2
=> 24 = k* 2^2
=> 24 = k * 4
=> Dividing by 4 on both sides we get k = 6
=> When x = 5 then Y = k x^2 = 6 * 5^2 = 6 * 25 = 150
=> Therefore, when x is 5 then the value of y is 150.