Direct and Inverse Variation

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

State 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

If y varies directly with x and y is 84 when x is 16, what is the equation representing this situation?

Back

y = 5.25x

Front

How does the number of painters affect 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 inverse variation?

Back

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

Front

Which graph represents direct variation?

Back

Graph C represents direct variation.

Front

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

Back

You can determine by checking if the ratio of y to x is constant (direct) or if the product of x and y is constant (inverse).