Direct, Inverse, and Joint 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 variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

What is joint variation?

Back

Joint variation is a relationship where a variable varies directly with the product of two or more other variables. It can be expressed as y = kxz, where k is a non-zero constant.

Front

If y varies directly as x and y = 10 when x = 2, what is the variation equation?

Back

y = 5x.

Front

If y varies inversely as x and y = 3 when x = 6, what is the variation equation?

Back

y = 18/x.

Front

What does the constant k represent in variation equations?

Back

The constant k represents the constant of variation, which is the factor by which one variable changes in relation to another.

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 for all values of x and y.

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 for all values of x and y.

Front

What is the equation for inverse variation when y = 4 and x = 2?

Back

y = 8/x.

Front

If y varies jointly as x and z, and y = 12 when x = 3 and z = 2, what is the variation equation?

Back

y = 2xz.