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.

Front

If y varies directly with x and k = 4, what is the equation?

Back

y = 4x

Front

If y varies inversely with x and k = 10, what is the equation?

Back

y = 10/x

Front

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

Back

To find the constant of variation in direct variation, divide y by x (k = y/x).

Front

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

Back

To find the constant of variation in inverse variation, multiply x and y (k = xy).

Front

What is the constant of variation if y = 3 when x = 1?

Back

k = 3 (since y = kx, k = y/x = 3/1).

Front

What is the constant of variation if y = 5 when x = 2?

Back

k = 10 (since y = k/x, k = xy = 5*2).

Front

Which graph represents direct variation?

Back

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

Front

Which graph represents inverse variation?

Back

A hyperbola that approaches the axes but never touches them.