4-2 Direct & 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 is calculated by dividing y by x (k = y/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 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 the constant of proportionality.

Front

If y varies jointly as x and z, and y = -180 when z = 15 and x = -3, what is the formula for y?

Back

y = kxz, where k can be calculated using the given values.

Front

How do you find the value of y when x = 7 and z = -5, given y varies jointly as x and z?

Back

First, find k using the initial values, then substitute x = 7 and z = -5 into the equation y = kxz.

Front

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

Back

y = 26

Front

What type of variation is represented by the equation y = kx?

Back

Direct variation.

Front

If y = kxz and y = -180 when z = 15 and x = -3, what is k?

Back

k = 4.

Front

What happens to y in direct variation if x is doubled?

Back

If x is doubled, y also doubles.