Direct/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 inversely as x and x=5 when y=20, what is the constant of variation, k?

Back

k = xy = 5 * 20 = 100.

Front

Which equation represents direct variation?

Back

y = kx.

Front

Which equation represents inverse variation?

Back

y = k/x.

Front

What is the constant of variation in the equation y = k/x if k = 12?

Back

The constant of variation is 12.

Front

Is the relationship between x and y in the table (x: 1, y: 12), (x: 2, y: 6), (x: 3, y: 4) direct or inverse variation?

Back

Inverse variation.

Front

If y = 4 when x = 2, what is the constant of variation for the direct variation?

Back

k = y/x = 4/2 = 2.

Front

What does it mean if a table shows direct variation?

Back

It means that as one variable increases, the other variable also increases proportionally.

Front

What does it mean if a table shows inverse variation?

Back

It means that as one variable increases, the other variable decreases, such that their product remains constant.