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, or y = k/x.

Front

If y varies directly as x and y = 10 when x = 2, what is the value of y when x = 5?

Back

y = 25.

Front

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

Back

y = 4.

Front

What does the constant of variation represent in direct variation?

Back

The constant of variation (k) represents the ratio of y to x, indicating how much y changes for a unit change in x.

Front

What does the constant of variation represent in inverse variation?

Back

The constant of variation (k) represents the product of x and y, indicating that as one variable increases, the other decreases.

Front

How can you determine if a relationship is a direct variation?

Back

A relationship is a direct variation if the ratio of y to x is constant for all pairs of values.

Front

How can you determine if a relationship is an inverse variation?

Back

A relationship is an inverse variation if the product of x and y is constant for all pairs of values.