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# Directvariation

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### Directvariation

1. 1. What do you guess? Eating too much Obesity
3. 3. 95% 3 hours 75% 2 hours 65% 1 hour 55% 0 hour Grade in Math test # of hours you study
4. 4. <ul><li>What is it called when each of the variable increase the other increase? </li></ul>
5. 5. Direct Variation I Math
6. 6. OBJECTIVES <ul><li>Understand what is direct variation and the constant of variation. </li></ul><ul><li>2) Know how to solve problems with direct variation : </li></ul><ul><li>+ Is an equation a direct variation ? </li></ul><ul><li>+ Writing an equation given a point </li></ul><ul><li>+ Direct variations and tables </li></ul><ul><li>+ Direct variation and graph </li></ul>
7. 7. Direct Variation What is it How can we know it ?
8. 8. A direct variation is a function in the form y = kx where k does not equal 0. Definition
9. 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
10. 10. An equation is a direct variation if: <ul><li>its graph is a line that passes through zero, or </li></ul><ul><li>the equation can be written in the form y = kx . </li></ul>
11. 11. Problem solving
12. 12. Is an equation a direct variation If it is, find the constant of variation
13. 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
14. 14. Practices <ul><li>2y = 5x + 1 -12x = 6y </li></ul>
15. 15. Writing an Equation Given a Point
16. 16. Example <ul><li>y = kx Start with the function form of the direct variation. </li></ul><ul><li>-3 = k(4) Substitute 4 for x and -3 for y. </li></ul><ul><li>k= -3/4 Divide by 4 to solve for k. </li></ul><ul><li>Substitute the value of k into the original formula. </li></ul>The Answer! Y= -3/4 x Write an equation of the direct variation that includes the point (4, -3).
17. 17. Practices Write an equation of the direct variation that includes the point ( -3, -6 )
18. 18. <ul><li>REAL WORLD PROBLEM SOLVING </li></ul>
19. 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
20. 20. Relate: The distance varies directly with the time. When x = 10, y = 2. <ul><li>Define: </li></ul><ul><li>Let x = number of seconds between seeing lightning and hearing thunder. </li></ul><ul><li>Let y = distance in miles from lightning. </li></ul><ul><li>y = kx ` Use general form of direct variation. </li></ul><ul><li>2 = k (10) Substitute 2 for y and 10 for x. </li></ul><ul><li>( Solve for k ) </li></ul><ul><li>Write an equation using the value for k . </li></ul>
21. 21. Direct Variation and tables
22. 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 .
23. 23. Which of the following is a direct variation? <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Answer Now
24. 24. Which is the equation that describes the following table of values? <ul><li>y = -2x </li></ul><ul><li>y = 2x </li></ul><ul><li>y = ½ x </li></ul><ul><li>xy = 200 </li></ul>Answer Now
25. 25. <ul><li>Using Direct Variation to find unknowns (y = kx) </li></ul>
26. 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. 27. Practices Given that y varies directly with x, and y = 6 when x=-5, Find y when x = -8. HOW???
28. 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. 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. 30. the ORIGIN!!!!!
31. 31. Tell if the following graph is a Direct Variation or not. No Yes No No
32. 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. 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. 34. HOMEWORK Finish the worksheet ( 3 , 4 , 6 , 7 , 9 , 10 , 11 , 12 )