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 the constant of proportionality.

Front

What is the constant of proportionality in direct variation?

Back

The constant of proportionality (k) is the constant factor that relates the two variables in a direct variation. It can be found by dividing y by x.

Front

If y varies directly with x and y = 84 when x = 16, what is k?

Back

k = 5.25

Front

What is joint variation?

Back

Joint variation occurs when a variable depends on two or more other variables. It can be expressed as y = kxz, where k is the constant of variation.

Front

If y varies jointly as x and z, and y = -180 when z = 15 and x = -3, what is y when x = 7 and z = -5?

Back

y = -140

Front

What is inverse variation?

Back

Inverse variation is a relationship where one variable increases as the other decreases. It can be expressed as y = k/x, where k is a constant.

Front

If y = 400/x, what is the constant k?

Back

k = 400

Front

If y = 15 when x = 32, what is y when x = 12?

Back

y = 40

Front

In a direct variation, if y = 39 when x = 3, what is y when x = 2?

Back

y = 26

Front

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

Back

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