Inverse and Direct variations

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 with x and y = 39 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 39/3 = 13.

Front

If y varies directly with x and k = 13, what is y when x = 2?

Back

y = kx = 13 * 2 = 26.

Front

In a direct variation, if x increases, what happens to y?

Back

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

Front

In an inverse variation, if x increases, what happens to y?

Back

In inverse variation, if x increases, y decreases.

Front

What type of variation is represented by the relationship between the length of time you charge your cell phone and the battery power?

Back

Direct variation.

Front

What type of variation is represented by the relationship between the outside temperature and the number of layers of clothes needed?

Back

Inverse variation.

Front

If Shawn's pay is $123 for 20 hours of work, what is the constant of variation (k)?

Back

k = 123/20 = 6.15.

Front

If the number of friends sharing the cost of pizzas increases, what happens to the amount each person pays?

Back

The amount each person pays decreases, indicating inverse variation.