Direct and Inverse 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 two variables is a constant. It can be expressed as y = k/x, where k is the constant of variation.

Front

If y varies directly as x and y = 10 when x = 5, what is the constant of variation?

Back

The constant of variation k is 2, since y = kx implies k = y/x = 10/5.

Front

If y varies inversely as x and y = 4 when x = 2, what is the constant of variation?

Back

The constant of variation k is 8, since y = k/x implies k = yx = 4*2.

Front

What is the equation of a direct variation if the constant of variation is 3?

Back

The equation is y = 3x.

Front

What is the equation of an inverse variation if the constant of variation is 5?

Back

The equation is y = 5/x.

Front

How do you determine if a set of points represents direct variation?

Back

A set of points represents direct variation if the ratio of y to x is constant for all points.

Front

How do you determine if a set of points represents inverse variation?

Back

A set of points represents inverse variation if the product of x and y is constant for all points.

Front

What does the graph of direct variation look like?

Back

The graph of direct variation is a straight line that passes through the origin (0,0).

Front

What does the graph of inverse variation look like?

Back

The graph of inverse variation is a hyperbola that approaches the axes but never touches them.