Direct & Inverse Variation

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is a non-zero constant.

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

It means that y increases as the square of z increases, and can be expressed as y = kz², where k is a constant.

The relationship can be expressed as y = kx²/z, where k is a constant.

If x is doubled, y also doubles, since y is directly proportional to x.

If x is halved, y will double, since y is inversely proportional to x.

k represents the constant of proportionality, which indicates how much y changes for a change in x.

To find k, use the equation: 10 = k/2, thus k = 20.

Using direct variation, set up the ratio: 60/90 = x/75. Solving gives x = 50 kg of water.

The formula for direct variation is y = kx, where k is a constant.