1. Proportional Techniques & Standard Graphs

2. Proportional Techniques

3. More complicated example

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6. Another example

7. Be a Thinker!

8. STANDARD GRAPHS

9. Standard Graphs - linear graphs A straight line passing through the origin shows proportionality y x y  x y = k x Where k is the constant of proportionality k = rise/run

10. Examples of direct proportionality graph Example 1:the extension of a spring against the weight on it. extension weight Courtesy to http://www.physics4u.co.uk/ How Science works--Graphshttp://www.physics4u.co.uk/How Science works--Graphs

11. Example 2:the current in a resistor against the p.d. across it. current voltage This illustrates Ohm’s Law. Examples of direct proportionality graph Courtesy to http://www.physics4u.co.uk/ How Science works--Graphshttp://www.physics4u.co.uk/How Science works--Graphs

12. Standard Graph- linear graphs A straight line with a y-intercept different than zero. The relationship between y and x is linear and not proportional y  x y = m x + b Where m is the slope of the line and b is the y-intercept y x b Slope = m

13. A straight line graph: Example of Linear Graphs An example would be the length of a spring against the weight on it. weight length weight Courtesy to http://www.physics4u.co.uk/ How Science works--Graphshttp://www.physics4u.co.uk/How Science works--Graphs

14. Standard Graphs – Power Graphs A power graph shows that y is directly proportional to x n (n> 1) y x y  x n

15. Power Graphs – example of Parabola A parabola is a power graph where n = 2. It shows that y is directly proportional to x 2 y x2x2 y x i.e. y  x 2 or y = kx 2 where k is the constant of proportionality

16. Example of a Power Graph- Parabola

17. Standard Graphs – Root Graphs

18. Example of a Root Graph- Period of a Pendulum

19. Standard Graphs – Inverse Graph (Hyperbola)

20. Standard Graphs - hyperbola P 1/V P V

21. Inverse Graph- Inverse Square Law g 1/R 2 g R