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 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.

Front

How do you identify direct variation from a table of values?

Back

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

Front

How do you identify inverse variation from a table of values?

Back

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

Front

What is the constant of variation in direct variation?

Back

The constant of variation in direct variation is the ratio k, which can be found by dividing y by x (k = y/x).

Front

What is the constant of variation in inverse variation?

Back

The constant of variation in inverse variation is the product k, which can be found by multiplying x and y (k = xy).

Front

If y varies directly as x and y = 20 when x = 4, what is the constant of variation?

Back

The constant of variation k is 5, since k = y/x = 20/4.

Front

If xy = 30, what is the value of y when x = 5?

Back

When x = 5, y = 6, since 5y = 30.

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 xy = k.