1. What do you guess? Eating too much Obesity

2. What do you guess? No studying Bad grade

3. 95% 3 hours 75% 2 hours 65% 1 hour 55% 0 hour Grade in Math test # of hours you study

5. Direct Variation I Math

7. Direct Variation What is it How can we know it ?

8. A direct variation is a function in the form y = kx where k does not equal 0. Definition

9. Y varies directly as x means that y = kx where k is the constant of variation. Another way of writing this is k = In other words: * the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.( k = the coefficient of x ) NOTES

11. Problem solving

12. Is an equation a direct variation If it is, find the constant of variation

13. Example y – 7.5x = 0 y – 7.5x + 7.5x = 0 + 7.5 x Y = 7.5x Yes, it’s a direct variation. Constant of variable, k , is Solve for y 7.5

15. Writing an Equation Given a Point

17. Practices Write an equation of the direct variation that includes the point ( -3, -6 )

19. Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the lightning. Write an equation for the relationship between time and distance

21. Direct Variation and tables

22. For each table, use the ratio y/x to tell whether y varies directly with x. If it does, write an equation for the direct variation Y / X 5/15 = 1/3 26/3 = 26/3 75 / 1 = 75 150 / 2 = 75 No , the ratio y / x is not the same for all pairs of data .

26. Given that y varies directly with x, and y = 28 when x=7, Find x when y = 52. HOW??? 2 step process 1. Find the constant variation k = y/x or k = 28/7 = 4 k=4 2. Use y = kx. Find the unknown (x). 52= 4x or 52/4 = x x= 13 Therefore: X =13 when Y=52

27. Practices Given that y varies directly with x, and y = 6 when x=-5, Find y when x = -8. HOW???

28. Given that y varies directly with x, and y = 6 when x=-5, Find y when x = -8. HOW??? 2 step process 1. Find the constant variation. k = y/x or k = 6/-5 = -1.2 k = -1.2 2. Use y = kx. Find the unknown (x). y= -1.2(-8) x= 9.6 Therefore: X =-8 when Y=9.6 Using Direct Variation to find unknowns (y = kx)

29. Direct Variation and its graph y = mx +b, m = slope and b = y-intercept With direction variation the equation is y = kx Note: m = k or the constant and b = 0 therefore the graph will always go through…

30. the ORIGIN!!!!!

31. Tell if the following graph is a Direct Variation or not. No Yes No No

32. GROUPS !!! With your group friends, come up with an interesting example that shows direct variation. ( 3 minutes ) FOR EXAMPLE : If you eat a lot , you will be fat

33. WHO IS FASTER ? 1 ) ONLY do the highlighted problems 2) You can do in pairs if you want 3) The 3 fastest people that finish all the problems with right answers will get the prize 1 st = 6 candies 2 nd = 4 candies 3 rd = 2 candies

34. HOMEWORK Finish the worksheet ( 3 , 4 , 6 , 7 , 9 , 10 , 11 , 12 )