Direct Variation
The quantity y is directly proportional to a quantity x if y=kx, where k is a constant, called the constant of variation.
Given that p varies directly as q, find an expression for p in terms of q if p=126 when q=7.
1. Since p varies directly as q, write p=kq
2. Since p=126 when q=7, substitute these values to obtain 126=k(7), or k=18.
3. Hence p=18q is the required expression.
y varies directly as the cube of x. If y=32 when x=2, find y when x=3.
y=kx^{3}
32=k(2)^{3} k=4 y=4x^{3}
Hence y=4(3)
^{3}=108 is the value of y when x=3
A ball is dropped from the top of a building. The distance the ball falls is directly proportional to the square of the time it has been failling. If a ball falls 48 feet in 2 seconds, find how far it has fallen after 6 seconds.
d=kt^{2} 48=k(2)^{2} 48=4k k=12 d=12t^{2}
Hence d=12(6)^{2}=432 is the distance the ball has fallen after 6 second.