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 mathematically as y = k/x, where k is a constant.

Front

If x and y vary inversely, what is the constant k when given the point (5, 20)?

Back

k = x * y = 5 * 20 = 100.

Front

How do you determine if an equation shows inverse variation?

Back

An equation shows inverse variation if it can be expressed in the form y = k/x, where k is a non-zero constant.

Front

Given that y varies inversely with x, if x = 7 and y = 4, what is y when x = 2?

Back

Using the constant k, k = x * y = 7 * 4 = 28. Then, when x = 2, y = k/x = 28/2 = 14.

Front

What is the relationship between the number of employees and the time to complete a project in inverse variation?

Back

As the number of employees increases, the time to complete the project decreases, and vice versa.

Front

If 3 people can complete a project in 7 days, how long will it take 5 people?

Back

Using inverse variation, t = (3 * 7) / 5 = 4.2 days.

Front

Back

This equation represents an inverse variation where y varies inversely with x, with a constant k = 10.

Front

Is the relationship between distance and time for a constant speed an example of inverse variation?

Back

No, it is an example of direct variation.

Front

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

Back

If x is doubled, y will be halved.

Front

What is the formula for inverse variation?

Back

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