Direct and Inverse 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 = 12 when x = 3, what is the constant of variation?

Back

k = y/x = 12/3 = 4.

Front

If y varies inversely with x and y = 5 when x = 2, what is the constant of variation?

Back

k = xy = 5 * 2 = 10.

Front

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

Back

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

Front

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

Back

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

Front

If the number of hours worked varies directly with the amount of money earned, and a person earns $300 for 10 hours, how much will they earn for 15 hours?

Back

They will earn $450.

Front

If the distance traveled varies directly with time at a constant speed, and a car travels 120 miles in 2 hours, how far will it travel in 5 hours?

Back

The car will travel 300 miles.

Front

If the pressure of a gas varies directly with its temperature, and the pressure is 200 atm at 100 degrees, what is the pressure at 200 degrees?

Back

The pressure will be 400 atm.

Front

If the time taken to complete a task varies inversely with the number of workers, and it takes 10 hours for 2 workers, how long will it take for 5 workers?

Back

It will take 4 hours.