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 constant. It can be expressed as y = k/x, where k is the constant of variation.

Front

If y varies directly as x and k = 3, what is the equation?

Back

y = 3x

Front

If y varies inversely as x and k = 12, what is the equation?

Back

y = 12/x

Front

What does the constant of variation represent in direct variation?

Back

The constant of variation (k) represents the ratio of y to x in a direct variation relationship.

Front

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

Back

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

Front

In the equation y = kx, what happens to y if x is doubled?

Back

If x is doubled, y will also double, since they are directly proportional.

Front

In the equation y = k/x, what happens to y if x is halved?

Back

If x is halved, y will double, since they are inversely proportional.

Front

What is the formula to find the distance required to stop a car if speed varies directly as the square of the speed?

Back

Distance = k * (speed)^2, where k is a constant.

Front

If a person weighing 80 kg has 50 kg of water, how much water does a person weighing 100 kg have if water varies directly with mass?

Back

62.5 kg of water.