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

Front

What does Boyle's Law state?

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 does gas pressure vary with temperature?

Back

Gas pressure varies directly with temperature; as temperature increases, pressure increases.

Front

If the pressure in a chamber is 150 atm at 50 degrees, what is the pressure at 75 degrees?

Back

225 atm

Front

What is the relationship between the number of painters and the time taken to paint a house?

Back

The number of hours to paint a house varies inversely with the number of painters working.

Front

If 6 painters can paint a house in 27 hours, how many painters are needed to paint it in 18 hours?

Back

9 painters

Front

What is the constant of variation in an inverse relationship?

Back

The constant of variation in an inverse relationship is the product of the two variables.

Front

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

Back

You can determine the type of variation by checking if the ratio of the variables is constant (direct) or if the product of the variables is constant (inverse).