# Variation & Problem Solving

Question Answer
If y varies directly as x, find the constant of variation and direct variation equation:

y is 5 and x is 30 =

y = kx,Substitute y and x in the equation,
5 = k.30; k = 5/30 ; k = 1/6. Substitute k in the direct variation equation = y = 1/6x.
Direct Variation :

y = 6 when x is 4 =

y = kx,Substitute y and x in the equation,
6 = k.4; k = 6/4 ; k = 3/2. Substitute k in the direct variation equation = y = 3/2x.
Direct Variation:

y = 0.2 when x is 0.8 =

y = kx,Substitute y and x in the equation,
0.2 = k.0.8; k = 0.2/0.8 ; k = 0.25. Substitute k in the direct variation equation = y = 0.25x
When y varies inversely as x or y is inversely proportional to x, find the constant of variation and inverse variation equation:

y = 6 when x = 5 =

y = k/x,Substitute y and x in the equation,
6 = k/5; k = ; k = 30. Substitute k in the inverse variation equation = y = 30/x.
Inverse Variation:

y = 0.2 when x = 0.7 =

y = k/x,Substitute y and x in the equation,
0.2 = k/0.7; k = ; k = 0.14. Substitute k in the inverse variation equation = y = 0.14/x.
Inverse Variation:

y = 1/8 when x = 16

y = k/x,Substitute y and x in the equation,
1/8 = k/16; k = ; k = 2. Substitute k in the inverse variation equation = y = 2/x.
y varies directly as square of x. If y is 24 when x is 2 find the constant of variation and variation equation? y = kx^2
24 = k. 2^2
24 = 4k
k = 6
Constant of variation is 6 and
Variation Equation is y = 6x^2