Direct, Inverse, Joint Variations

Front

What is Direct Variation?

Back

Direct variation is a relationship between two variables in which 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 in which 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 two or more other variables. It can be expressed as z = kxy, where k is a non-zero constant.

Front

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

Back

y = 25.

Front

If y varies inversely as x and y = 4 when x = 3, what is y when x = 6?

Back

y = 2.

Front

If V varies jointly as h and d^2, and V = 15.84 when h = 22 and d = 3, what is V when h = 32 and d = 4?

Back

V = 40.96 ft³.

Front

What is the formula for Direct Variation?

Back

The formula for direct variation is y = kx.

Front

What is the formula for Inverse Variation?

Back

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

Front

What is the formula for Joint Variation?

Back

The formula for joint variation is z = kxy.

Front

If m varies directly as p, and m = 35 when p = 5, what is the constant of variation k?

Back

k = 7.