Inverse Variation

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables, x and y, such that when one variable increases, the other decreases. It can be expressed as y = k/x, where k is a constant.

Front

If y varies inversely as x, what is the formula used to express this relationship?

Back

The formula for inverse variation is y = k/x, where k is the constant of variation.

Front

What does the constant of variation (k) represent in inverse variation?

Back

The constant of variation (k) represents the product of the two variables in an inverse relationship. It remains constant for all pairs of (x, y) values.

Front

If y = 23 when x = 8, what is the constant of variation (k)?

Back

To find k, use the formula k = xy. Here, k = 23 * 8 = 184.

Front

Given x = 5 when y = 20, find the constant of variation (k).

Back

k = xy = 5 * 20 = 100.

Front

If x = 6 when y = 9, what is the constant of variation (k)?

Back

k = xy = 6 * 9 = 54.

Front

In an inverse variation, if y = 4 when x = 2, what is y when x = 8?

Back

Using k = xy, k = 4 * 2 = 8. Then, y = k/x = 8/8 = 1.

Front

How can you determine if a table of values represents an inverse variation?

Back

A table represents inverse variation if the product of each pair of (x, y) values is constant.

Front

If y varies inversely as x and k = 12, what is y when x = 3?

Back

Using the formula y = k/x, y = 12/3 = 4.

Front

What is the missing value of y if x = 4 and k = 12?

Back

Using y = k/x, y = 12/4 = 3.