1. What do you guess?

3. # of hours you studyGrade in Math test 0 hour55% 1 hour65% 2 hours75% 3 hours95%

4. What is it called when each of the variable increase the other increase?

5. I Math

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

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

8. 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

9. An equation is a direct variation if:  its graph is a line that passes through zero, or  the equation can be written in the form y = kx.

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

12. 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

13. Practices 2y = 5x + 1 -12x = 6y

14. Writing an Equation Given a Point

15. Example y = kx Start with the function form of the direct variation. -3 = k(4) Substitute 4 for x and -3 for y. k= -3/4 Divide by 4 to solve for k. Substitute the value of k into the original formula. Y= -3/4 x Write an equation of the direct variation that includes the point (4, -3).

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

17. REAL WORLD PROBLEM SOLVING

18. 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

19. Relate: The distance varies directly with the time. When x = 10, y = 2. Define: Let x = number of seconds between seeing lightning and hearing thunder. Let y = distance in miles from lightning. y = kx `Use general form of direct variation. 2 = k(10)Substitute 2 for y and 10 for x. ( Solve for k ) Write an equation using the value for k.

20. Direct Variation and tables

21. 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.

22. Which of the following is a direct variation? 1.A 2.B 3.C 4.D Answer Now

23. Which is the equation that describes the following table of values? 1.y = -2x 2.y = 2x 3.y = ½ x 4.xy = 200 Answer Now

24. Using Direct Variation to find unknowns (y = kx)

25. 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

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

27. 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)

28. 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…

29. the ORIGIN!!!!!

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