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 joint variation?

Back

Joint variation occurs when a variable varies directly with two or more other variables. It can be expressed as y = kxz, where y varies jointly with x and z, and k is the constant of proportionality.

Front

If a varies jointly as b and c, and a = 15 when b = 4 and c = 5, what is the equation for a?

Back

The equation is a = kbc. To find k, substitute the values: 15 = k(4)(5) => k = 0.75. Thus, a = 0.75bc.

Front

If y varies directly with x and y = 84 when x = 16, what is the constant of proportionality (k)?

Back

k = y/x = 84/16 = 5.25.

Front

What is the formula for inverse variation?

Back

Inverse variation is expressed as y = k/x, where k is a constant.

Front

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

Back

The equation is y = kxz. To find k, substitute the values: -180 = k(-3)(15) => k = 4.

Front

If y = kxz and k = 4, what is y when x = 7 and z = -5?

Back

y = 4(7)(-5) = -140.

Front

What does it mean if a variable varies inversely?

Back

It means that as one variable increases, the other decreases, and vice versa, maintaining a constant product.

Front

If y varies inversely with x, and y = 10 when x = 2, what is the equation for y?

Back

The equation is y = k/x. To find k, substitute the values: 10 = k/2 => k = 20. Thus, y = 20/x.

Front

What is the relationship between direct variation and proportionality?

Back

In direct variation, the two variables are proportional to each other, meaning their ratio is constant.