Direct and inverse variation word problems

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 or y = k/x, where k is a non-zero constant.

Front

How do you determine if a problem involves direct variation?

Back

A problem involves direct variation if one variable increases or decreases in direct proportion to another variable.

Front

How do you determine if a problem involves inverse variation?

Back

A problem involves inverse variation if one variable increases while the other decreases, such that their product remains constant.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

What is the formula for inverse variation?

Back

The formula for inverse variation is y = k/x, where k is the constant of variation.

Front

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

Back

k = y/x = 10/2 = 5.

Front

If the number of gallons g varies directly with the number of miles m, and g = 12 when m = 270, how many gallons are needed for 400 miles?

Back

g = k * m; k = 12/270; g = (12/270) * 400 = 18 gallons.

Front

If the volume V of a gas varies inversely with the pressure p, and V = 15 when p = 24, what is the constant k?

Back

k = V * p = 15 * 24 = 360.

Front

If V = 360 when p = 30, what is the volume when the pressure is 30 pounds per square inch?

Back

V = k/p = 360/30 = 12 cubic feet.