Inverse Variation

Front

What is Inverse Variation?

Back

Inverse Variation describes a relationship between two variables where an increase in one variable results in a decrease in the other, and vice versa. It can be expressed as y = k/x, where k is a constant.

Front

What is the constant of variation in inverse variation?

Back

The constant of variation (k) in inverse variation is the product of the two variables. If y varies inversely with x, then k = xy.

Front

If y varies inversely with x, and x = 3 when y = 6, what is the constant of variation?

Back

k = xy = 3 * 6 = 18.

Front

How do you determine if a table represents inverse variation?

Back

A table represents inverse variation if the product of the paired values (x and y) is constant.

Front

What is the formula for inverse variation?

Back

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

Front

If y = 20 when x = 4, what is y when x = 5 in inverse variation?

Back

Using k = xy, k = 20 * 4 = 80. When x = 5, y = 80/5 = 16.

Front

What happens to y if x is doubled in an inverse variation?

Back

If x is doubled, y will be halved, since they vary inversely.

Front

What is the relationship between direct and inverse variation?

Back

In direct variation, y = kx, while in inverse variation, y = k/x. They represent opposite relationships between the variables.

Front

If the cost per person to rent a cabin is inversely proportional to the number of people, what happens as more people join?

Back

As more people join, the cost per person decreases.

Front

What type of variation is represented by the equation y = 400/x?

Back

This equation represents inverse variation.