Direct & Inverse Variation

Front

What is direct variation?

Back

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.

Front

What is inverse variation?

Back

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.

Front

What does it mean if y is directly proportional to z squared?

Back

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

Front

How do you represent a situation where y varies directly as the square of x and inversely as z?

Back

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

Front

If y = kx, what happens to y if x is doubled?

Back

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

Front

If y = k/x, what happens to y if x is halved?

Back

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

Front

In the equation y = kx, what does k represent?

Back

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

Front

What is the constant of variation in the equation y = k/x if y = 10 when x = 2?

Back

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

Front

If a person weighing 90 kg has 60 kg of water, how much water does a 75 kg person have?

Back

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

Front

What is the formula for direct variation?

Back

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