Direct and 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 xy = k, where k is a non-zero constant.

Front

What is the formula for direct variation?

Back

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

Front

What is the formula for inverse variation?

Back

The formula for inverse variation is xy = k, where k is the constant.

Front

If y varies directly as x and y = 10 when x = 2, what is the value of k?

Back

k = 5.

Front

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

Back

y = 4.

Front

How do you find the constant of variation in direct variation?

Back

To find the constant of variation (k), divide y by x (k = y/x).

Front

How do you find the constant of variation in inverse variation?

Back

To find the constant of variation (k), multiply x and y (k = xy).

Front

What does it mean if two variables are directly proportional?

Back

If two variables are directly proportional, as one variable increases, the other variable also increases at a constant rate.

Front

What does it mean if two variables are inversely proportional?

Back

If two variables are inversely proportional, as one variable increases, the other variable decreases, such that their product remains constant.