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Monday, April 23 rd

Monday, April 23 rd. Warm UP. What is k? Y=3/4x What point does a direct Variation equation have to go through?. Please complete Warm up. Last March Madness. Denman Test 10: Measurement & Geometry. FORMULA SHEET . a = Bh. l x w. Rectangular Prism:. Cylinder Prism:. Direct

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Monday, April 23 rd

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  1. Monday, April 23rd Warm UP What is k? Y=3/4x What point does a direct Variation equation have to go through? Please complete Warm up

  2. Last March Madness Denman Test 10: Measurement & Geometry

  3. FORMULA SHEET a=Bh l x w Rectangular Prism: Cylinder Prism:

  4. Direct Variation

  5. y=kx

  6. What is k? Give the value shown for k • Y = 4x • Y=1/2x • Y=.75x • Y=x 4 1/2 .75 1

  7. Recap • A Linear equation makes a LINE when graphed • Y= kxis a special kind of LINEAR equation • Y=kx must go through (0,0) • In an equation we always put in a number for k (y=2x) • K is our slope (how steep the line is)

  8. Part I: Determining if a function is a Direct Variation

  9. Which one is a direct variation?

  10. Which one is a direct variation?

  11. Direct variation equation • Equation can not have anything added or subtracted to it. • Remember that y=x/4 is the same as y = 1/4 x

  12. Which Equation(s) are examples of direct variation? • Y= 3x+2 • Y= • Y= 0.85x • Y= • Y= 443x 2 3 And 5 *Nothing can be added or subtracted!

  13. Part II: Finding K in a Table

  14. Finding K K = y ÷ x

  15. Example #1 Answer: k=4

  16. Example #2 Answer: k=1/4

  17. Example #3 Answer: k=5/2 or 2 ½

  18. EXCITING NEWS!!! Now that we know how to find k in a table, we can look at a table to see if it’s truly a direct variation!!! Steps: • For each ordered pair, divide y by x and make sure it’s the same number! • If it’s not then it isn’t a direct variation

  19. Which table shows a Direct Variation?

  20. Graphing

  21. Where is the origin?!?!

  22. Do You Remember? • Which axis is the horizontal axis? _____________ • Which axis is the vertical axis? _____________

  23. K= Slope When you think of the word SLOPE…what do you think of?!

  24. Slopes are commonly associated with mountains

  25. The slope we are studying is associated with the graph of a line

  26. Different Slopes zero Positive Undefined Negative

  27. POSITIVE SLOPE“Reaching the Goal”

  28. Negative Slope“The Tumbler”

  29. Zero Slope“Not Much Happening” Horizontal Line

  30. We will only be working with POSTIVE SLOPES that go through the point (0,0)

  31. K= Rise ÷ Run Rise= y axis Run= x axis

  32. What goes first? You need to rise up before you run

  33. Finding Slope “The Meat of it”

  34. Find k (slope) Slope: Rise: 3 Run: 2 k: 3/2 Y=3/2x

  35. Find k (slope) Slope: Rise: 3 Run: 1 k: 3/1= 3 Y=3x

  36. Find k (slope) Slope: Rise: 2 Run: 3 k: 2/3= 2/3 Y=2/3x

  37. Find k (slope) Slope: Rise: 1 Run: 5 k: 1/5= 1/5 Y=1/5x

  38. The steeper the line is the larger K will be!

  39. SO. . . If you graphed each set of equations below, all of the graphs would be straight lines. For each group of equations, the steepest line would be represented by which equation? • y = 3x B. y = 9x Cy = x D. y = 4x

  40. The cost of a plane ticket varies directly with the amount of people. The cost for 5people costs $500. What is the constant of variation? Write an equation that represents this situation K=500/5 =100 Y=100x

  41. Leigh Parker earns $30 for every 3 chores she does. If x represents the number of chores she does, write an equation that will tell how many dollars (y) she will earn. K=30/3 =10 Y=10x

  42. The equation: y = 7x can be used to determine how much money you make when babysitting. Where y (the total amount you make) varies directly with x (the number of hours you babysat). If you babysat 10 hours, how much money would you make?

  43. Answer Since x = hours substitute 10 in for x in your equation. Y = 7(10) Y=70 You would make $70

  44. Murphy earns $40 for every 2 dogs she walks. Write an equation that will tell how many dollars she will earn.

  45. Answer 1. Make y equal money earned since it is dependent 2. Make x equal to the number of dogs she walked since it’s independent 3. Find the CONSTANT: y/x 40/2 = 20 k=20 4. Write an equation: y=20x

  46. Produce a table and graph for y=4x

  47. Answer: Table

  48. The cost of a ticket for the hunger games varies directly with how many tickets you buy. The cost for 6 people is $54. What is the constant?

  49. Y=1/4x What x values would you want to use?!?!?! 4 1 8 2 12 3 16 4 You would want to use multiples of 4, since 4 is the denominator! That way you have whole numbers for your y values 

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