In Class 3a
Name: ________________ Block: _____
Algebra 2, Unit 5, Direct and Inverse Variation
1. The value of y varies directly with x, and y = 20 when x = 2. Find y when x = 8. Or “y is proportional to x,
and y = 20 when x = 2. Find y when x = 8.”
2. The amount of money raised at a school fundraiser is directly proportional to the number of people who
attend. Last year, the amount of money raised for 100 attendees was $2500. How much money will be
raised if 1000 people attend this year?
In Class 3a
Name: ________________ Block: _____
Algebra 2, Unit 5, Direct and Inverse Variation
1. Use the following information to find the constant of proportionality. Write an equation that models the
information. Suibhne and Rishi have to drive 100 miles to get to their friend's lake cabin.
a) How many hours will it take them if they
o hike there at 4 mi/hr?
o Bike there at 20 mi/hr?
o drive there using the back roads at 50 mi/hr?
o drive there on the interstate at 75 mi/hr?
b) How fast do they need to travel if they want to get there in 1 hour?
2. y varies inversely as x, and y = 4 when x = 10. Write the inverse variation function. What is the value of y
when x = 20?
3. The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it
takes 2 hours for a square inch of ice to melt at 65º, find the constant of proportionality.
A relationship that contains both direct variation and inverse variation is called Combined Variation.
Quantities that vary directly appear in the numerator, and quantities that vary inversely appear in the
denominator.
4. The volume of a gas varies inversely as the pressure P and directly as the temperature T. A certain gs has a
volume of 10 liters (L), a temperature of 300 kelvins (K), and a pressure of 1.5 atmospheres (atm). If the
gas is heated to 400K and has a pressure of 1 atm, what is it’s volume?