1. Direct & Inverse Variation
EQ: How does a “direct” relationship between two variables compare to an “inverse” relationship between two variables?

2. Direct Variation As x increases, y increases
As x decreases, y decreases
When x = 0, y = 0

3. Inverse Variation As x increases, y decreases
As x decreases, y increases
Never equals zero

4. Quick Write – 1 minute
Think of something in your life that varies directly (increase-increase or decrease- decrease) and describe the relationship
Think of something in your life that varies inversely (increase-decrease or decrease- increase) and describe that relationship

5. Direct Inverse k = “constant of variation” SOLVE FOR ‘k’

6. Find the constant of variation (Direct)
1) 6 = k(5)
2) = k(0.2)
3) 4 = k(8)

7. Find the constant of variation (Inverse)1) 2) 3)

8. Ex 1) If y = -6 when x = -2 find y when x = 4 if…
a. y varies directly with x

9. b. y varies inversely with x

10. Ex 2) If y = 14 when x = 2, find y when x = 4 if…
a. y varies directly with x

11. b. y varies inversely with x

12. Ex 3) z varies directly with x and inversely with y
Ex 3) z varies directly with x and inversely with y. When x = 5 and y = 2, z = 10. Find z when x = 4 and y = 8

13. Problem #1
The volume V of a gas varies inversely as its pressure P. If V = 80 cubic centimeters when P = millimeters of mercury, find V when P = 320 millimeters of mercury.

14. Problem #2
The length S that a spring will stretch varies directly with the weight F that is attached to the spring. If a spring stretches 20 inches with 25 pounds attached, how far will it stretch with 15 pounds attached

15. Problem #3
The number of bags of grass seed n needed to reseed a yard varies directly with the area a to be seeded and inversely with the weight w of a bag of seed. If it takes two 3-lb bags to seed an area of 3,600 ft2, how many 3-lb bags will seed 9000 ft2 ?

16. Practice
Check your answers at one of the solution stations

17. The current in a simple electrical circuit is inversely proportional to the resistance. If the current is 80 amps when the resistance is 50 ohms, find the current when the resistance is 22 ohms.
amps

18. Your weight on Mars varies directly with your weight on Earth
Your weight on Mars varies directly with your weight on Earth. A person weighing 125 lbs on Earth weighs lbs on Mars, since Mars has less gravity. If you weigh 140 lbs on Earth, how much will you weigh on Mars? lbs

19. The frequency of a vibrating guitar string varies inversely as its length. Suppose a guitar string meters long has a frequency of 4.3 per second. What frequency would a string 0.5 meters long have?
5.59 per second

20. There are about 200 calories in 50 grams of Swiss cheese
There are about 200 calories in 50 grams of Swiss cheese.  Willie ate 70 grams of this cheese.  About how many calories were in the cheese that he ate if the number of calories varies directly as the weight of the cheese.
280 calories

21. The number of hours h that it takes m men to assemble x machines varies directly as the number of machines and inversely as the number of men. If four men can assemble 12 machines in four hours, how many men are needed to assemble 36 machines in eight hours?
6 men