1. Direct & Inverse Variations
Sections 2-5 & 8-1

2. I can recognize and solve direct variation word problems.
Objectives
I can recognize and solve direct variation word problems.
I can recognize and solve inverse variation word problems

3. As one variable increases, the other must also increase ( up, up)
Direct Variation
As one variable increases, the other must also increase ( up, up) OR
As one variable decreases, the other variable must also decrease. (down, down)

4. Real life?
With a shoulder partner take a few minutes to brainstorm real life examples of direct variation. Write them down.
Food intake/weight
Exercise/weight loss
Study time/ grades
Hourly rate/paycheck size
Stress level/blood pressure
Recipes
Paint Mixtures
Drug Manufacturing

5. Direct Variation k is the constant of variation
the graph must go through the origin (0,0) and must be linear!!

6. K: Constant of Variation
What does K really represent in direct variation??

7. Direct Variation
Ex 1)If y varies directly as x and y = 12 when x = 3, find y when x = 10.

8. FIRST: Find your data points!
Solving Method #1
FIRST: Find your data points!
(x,y)
NEXT: Solve for k & write your equation
LAST: use your “unknown” data point to solve for the missing variable.

9. FIRST: Find your data points!
Solving Method #2
FIRST: Find your data points!
(x,y)
NEXT: substitute your values correctly
LAST: cross multiply to solve for missing variable.

10. What did we do? EITHER ONE WILL WORK!! ITS YOUR CHOICE!
FIRST: Find your data points!
(x,y)
NEXT: Solve for k & write your equation
LAST: use your “unknown” data point to solve for the missing variable.
EITHER ONE WILL WORK!!
ITS YOUR CHOICE!
FIRST: Find your data points!
(x,y)
NEXT: substitute your values correctly
LAST: cross multiply to solve for missing variable.

11. Direct Variation Application
Ex: In scuba diving the time (t) it takes a diver to ascend safely to the surface varies directly with the depth (d) of the dive. It takes a minimum of 3 minutes from a safe ascent from 12 feet. Write an equation that relates depth (d) and time (t). Then determine the minimum time for a safe ascent from 1000 feet?

12. Your TURN #1 on Homework
Find y when x = 6, if y varies directly as x and y = 8 when x = 2.

13. As one variable increases, the other decreases. (or vice versa)
Inverse Variation
As one variable increases, the other decreases. (or vice versa)

14. Inverse Variation This is a
NON-LINEAR function (it doesn’t look like y=mx+b)
It doesn’t even get close to (0, 0)
k is still the constant of variation

15. Real life? Driving speed and time
With a shoulder partner take a few minutes to brainstorm real life examples of inverse variation. Write them down.
Driving speed and time
Driving speed and gallons of gas in tank
Pressure versus Volume
Water Depth versus Time of dive

16. Inverse Variation
Ex 3) Find y when x = 15, if y varies inversely as x and when y = 12, x = 10.

17. Solving Inverse Variation
FIRST: Find your data points!
(x,y)
NEXT: Find the missing constant, k,by using the full set of data given
LAST: Using the formula and constant, k, find the missing value in the problem

18. FIRST: Find your data points!
Method #2
FIRST: Find your data points!
(x,y)
NEXT: substitute your values correctly
LAST: use algebra to solve for missing variable.

19. What did we do? EITHER ONE WILL WORK!! ITS YOUR CHOICE!
FIRST: Find your data points!
(x,y)
NEXT: Find the missing constant, k,by using the full set of data given
LAST: Using the formula and constant, k, find the missing value in the problem
FIRST: Find your data points!
(x,y)
NEXT: substitute your values correctly
LAST: use algebra to solve for missing variable.
EITHER ONE WILL WORK!!
ITS YOUR CHOICE!

20. Inverse Variation Application
Ex:The intensity of a light “I” received from a source varies inversely with the distance “d” from the source. If the light intensity is 10 ft-candles at 21 feet, what is the light intensity at 12 feet? Write your equation first.

21. Your TURN #2 on Homework
Find x when y = 5, if y varies inversely as x and x = 6 when y = -18.

22. ½ Sheet Data Examine the data that you have comparing two variables.
Determine if the data varies directly or inversely or neither.
After determining the type of variation, find the constant of variation and answer the question.

23. Group Work Get into groups based on your question number.
Compare the answers that you each found and be prepared to present finding to the class.
You will present under the document camera

24. Direct vs. Inverse Variation

25. Homework
WS 1-3
Quiz next class on Parent Functions