Variation

Front

What is variation in mathematics?

Back

Variation refers to the way in which a quantity changes in relation to another quantity. It can be direct or inverse.

Front

Define direct variation.

Back

Direct variation occurs when two quantities increase or decrease together, represented by the equation y = kx, where k is the constant of variation.

Front

Define inverse variation.

Back

Inverse variation occurs when one quantity increases while the other decreases, represented by the equation y = k/x, where k is the constant of variation.

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, denoted as k.

Front

What is the constant of variation in inverse variation?

Back

The constant of variation in inverse variation is the product of the two variables, denoted as k.

Front

If y varies directly with x and y = 12 when x = 3, what is k?

Back

k = y/x = 12/3 = 4.

Front

If y varies inversely with x and y = 10 when x = 2, what is k?

Back

k = y * x = 10 * 2 = 20.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx.

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is y = k/x.

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.