Direct and Inverse Variations

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 the constant of variation.

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 the constant of variation.

Front

If y varies directly as x, what happens to y if x is doubled?

Back

If x is doubled, y also doubles.

Front

If y varies inversely as x, what happens to y if x is doubled?

Back

If x is doubled, y is halved.

Front

What is the constant of variation in direct variation?

Back

The constant of variation in direct variation is the ratio of y to x, represented as k = y/x.

Front

What is the constant of variation in inverse variation?

Back

The constant of variation in inverse variation is the product of x and y, represented as k = xy.

Front

How do 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.

Front

How do 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.

Front

Solve for y: y varies directly as x, and y = 10 when x = 2. What is y when x = 5?

Back

y = 25.

Front

Solve for y: y varies inversely as x, and y = 4 when x = 3. What is y when x = 6?

Back

y = 2.