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, typically expressed as y = kx, where k is a non-zero constant.

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant, typically expressed as y = k/x, where k is a non-zero constant.

Front

What is the general form of the equation for direct variation?

Back

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

Front

What is the general form of the equation for inverse variation?

Back

The general form of the equation for inverse variation is y = k/x, where k is a constant.

Front

How can you identify a direct variation graph?

Back

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

Front

How can you identify an inverse variation graph?

Back

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

Front

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

Back

To find k, use the equation y = kx. Here, 10 = k(2) => k = 5.

Front

If y varies inversely with x and y = 4 when x = 3, what is the constant of variation k?

Back

To find k, use the equation y = k/x. Here, 4 = k/3 => k = 12.

Front

What happens to y when x increases in a direct variation?

Back

In direct variation, as x increases, y also increases.

Front

What happens to y when x increases in an inverse variation?

Back

In inverse variation, as x increases, y decreases.