1. Advance Proportions
Unit 1 - Science

2. Advanced Proportions Sometimes the variables in a proportion have…
exponents

3. Advanced Proportions If Y is directly proportional to X then…
…If X doubles, Y will _______________. 2
Quadruple

4. Equation: Y= 2 k X

5. How do I solve for K?
Graph Y vs. 2 X
& the slope = k

6. Natural Graph vs. Linearized Graph
LINERIZED GRAPH: Y Y X x 2

7. Example:
You are curious if there is a relationship between the stretch distance of a tennis-ball launcher and how high the ball goes. You play with a launcher all afternoon and record the following data…

8. Here is the data you collect:
Stretch (m)
Height (m) .1
1.5 .2 6 .3 15 .4 26 .5 42

9. Graph the information on the first graph grid in your notes.

10. Your graph should look similar to this:
How the stretch distance affects the height of a tennis-ball
Height (m)
Stretch (m)

11. Now we need to linearize the graph:
To do this we will graph X2 and Y.
First we need to change our data table.

12. Our new data table will look like this:X2 Y
(.1)2 = .01
1.5
(.2)2 = .04 6
(.3)2 = .09 15
(.4)2 = .16 26
(.5)2 = .25 42

13. Graph the information on the second graph grid in your notes.

14. Your graph should look similar to this:X2

15. Next Steps: Write the EQUATION FORM: Y= kx2 Circle your cross points.
Solve for K.
K = (50-25)/( ) = 25/.15 =

16. So our real world equation is:
H =
166.67 s 2
Where H is the height & s is the stretch distance.

17. Summing it up!
Based on the shape of your graph, the height of the ball is directly proportional to stretch2 .
This means if you stretch THREE times longer you will launch 9 times higher!
Use your real world equation to predict how high the tennis ball will go if you stretch the launcher 0.75 meters.
Answer: meters high

18. Now try it on your own! Go back to your car graph from the basic graphs lab and determine the real world equation.

19. Advanced Proportions If Y is inversely proportional to X then…
…If X doubles, Y will _______________. 2
1/4

20. Equation: Y= k __ X2

21. How do I solve for K?
Graph Y vs. 1 __ X2
& the slope = k

22. Natural Graph vs. Linearized GraphY Y X
1/X2

23. Example:
You are curious if there is a relationship between the intensity of sunlight and the distance a planet is from the sun. You send out space probes and collect the following data…

24. Here is the data you collect:
Distance (AU)
Sunlight (W/m2 )
0.4
6800 1
986
1.5
438
5.2 36 40
0.6

25. Graph the information on the first graph grid in your notes.

26. Your graph should look similar to this:
Sunlight vs. Planet Distance
Sunlight (W/m2 )
Distance (AU)

27. Now we need to linearize the graph:
To do this we will graph 1/x2 and Y.
First we need to change our data table.

28. Our new data table will look like this:
1/x2 Y
1/(.4)2 = 6.25
6800
1/(1)2 = 1
986
1/(1.5)2 = 0.44
438
1/(5.2)2 = 0.04 36
1/(40)2 =
0.6

29. Graph the information on the second graph grid in your notes.

30. Your graph should look similar to this:
1/x2

31. Next Steps: Write the EQUATION FORM: Y= k/x2 Circle your cross points.
Solve for K.
K = ( )/(4-2) = 2100/2 = 1050

32. So our real world equation is:
1050
____ d2
Where S is the sunlight & d is the distance.

33. Summing it up!
Based on the shape of your graph, the intensity of sunlight is inversely proportional to distance2 .
This means if a planet is FOUR times further from the sun, the light will be 1/16 times as bright!
Use your real world equation to predict how much sunlight Venus gets if it is 0.72 AU from the sun.
Answer: W/m2

34. Now answer the questions to the real world application at the bottom of the page.

35. Now let’s do a real world application
Now let’s do a real world application. Follow the instructions for the Slinky Lab found on the previous page.