Direct and Inverse Variation

Front

What is Direct Variation?

Back

Direct Variation is a relationship between two variables where an increase in one variable results in a proportional increase in 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 an increase in one variable results in a proportional decrease in the other. It can be expressed as xy = k, where k is the constant of variation.

Front

What is Boyle's Law?

Back

Boyle's Law states that for a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to the pressure.

Front

If a gas occupies 9.84 liters at a pressure of 50 cm Hg, what is the pressure when the volume is increased to 12 liters?

Back

41.0 cm Hg

Front

How do you determine if a table represents direct or inverse variation?

Back

To determine if a table represents direct or inverse variation, check if the ratio of y to x is constant (direct) or if the product of x and y is constant (inverse).

Front

What is the constant of variation in inverse variation?

Back

The constant of variation in inverse variation is the product of the two variables, which remains constant.

Front

Which graph represents direct variation?

Back

A graph that passes through the origin and has a straight line indicates direct variation.

Front

If the time to fly varies inversely with speed, how do you calculate the time at a different speed?

Back

Use the formula: Time1 * Speed1 = Time2 * Speed2 to find the new time.

Front

If a trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

Back

6.75 hours

Front

How does the number of painters affect the time to paint a house?

Back

The time to paint a house varies inversely with the number of painters; more painters reduce the time required.