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 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. It can be expressed as xy = k, where k is a non-zero constant.

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, or y = \frac{k}{x}.

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

What does the constant k represent in direct variation?

Back

In direct variation, k represents the constant of variation, which indicates how much y changes for a unit change in x.

Front

What does the constant k represent in inverse variation?

Back

In inverse variation, k represents the constant product of the two variables, meaning that as one variable increases, the other decreases.

Front

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

Back

k = \frac{y}{x} = \frac{10}{2} = 5.

Front

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

Back

y = \frac{12}{x} = \frac{12}{3} = 4.