Direct, Joint, Inverse and Combined 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

If y varies directly as x and y = 22.5 when x = 15, what is the value of y when x = 20?

Back

30

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 j = k/m, where k is a non-zero constant.

Front

If j varies inversely with m and j = 60 when m = 0.3, what is the value of j when m = -2?

Back

-9

Front

What is joint variation?

Back

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

Front

If a varies jointly as b and c, and a = 15 when b = 4 and c = 5, what is the value of b when a = 60 and c = 5?

Back

16

Front

What is combined variation?

Back

Combined variation is a relationship that involves both direct and inverse variation. It can be expressed as y = kx/m, where k is a non-zero constant.

Front

If f varies directly as g and inversely as h, and f = -12 when h = 4 and g = -3, what is the value of g when f = 28 and h = 8?

Back

14

Front

How do you find the constant of variation in direct variation?

Back

To find the constant of variation (k) in direct variation, divide y by x (k = y/x).

Front

How do you find the constant of variation in inverse variation?

Back

To find the constant of variation (k) in inverse variation, multiply j by m (k = jm).