Direct, Inverse, Joint, & 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 the constant of variation.

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 xy = k, where k is the constant of variation.

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 z = kxy, where k is the constant of variation.

Front

What is Combined Variation?

Back

Combined variation is a relationship that involves both direct and inverse variation. It can be expressed as z = k rac{x}{y}, where k is the constant of variation.

Front

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

Back

To find the constant of variation in direct variation, use the formula k = rac{y}{x} for any ordered pair (x, y).

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

Back

To find the constant of variation in inverse variation, use the formula k = xy for any ordered pair (x, y).

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx, where k is the constant of variation.

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is xy = k, where k is the constant of variation.

Front

If y varies directly with x and y = 10 when x = 2, what is the constant of variation?

Back

k = rac{y}{x} = rac{10}{2} = 5.

Front

If xy = 12 and x = 3, what is the value of y?

Back

y = rac{12}{x} = rac{12}{3} = 4.