slope of a line

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slope of a line

  1. 1. It was a typical Monday for Garfield.
  2. 2. He slept all day long, dreaming of him
  3. 3. in a carnival with Pooky, his bestfriend toy.
  4. 4. That was the best rollercoaster ride ever!
  5. 5. Hmm.. I wonder where Pooky is.
  6. 6. Maybe I left him on the bed again.
  7. 7. Where’s Pooookkkyyyy?! I left him on my bed and now he’s gone!
  8. 8. I knew it! That Odie is making fun out of me. And he left a letter. How sweet!
  9. 9. He said that the only way I could get Pooky back is to play his game. Darn!
  10. 10. What’s up pussy?! Wanna play a game? I got one and it is starting now. I got your Pooky. Let me give you a clue on how to get to my next love letter that will tell where Pooky is. But you gotta need some Mathematics skills. Here’s the first clue:
  11. 11. Here are two points in a linear function. Its slope will tell you the number of steps you must take, 53O east of south from your bedroom. You better get the answer fast or else you wouldn’t get Pooky back! (-7,18), (-10, -12) (Click the paw print to return to Garfield)
  12. 12. Hmmm… that was quite difficult. But I think I can solve it.
  13. 13. Slope? What’s a slope? Aahhh yes! It’s the lesson Mr. De Guzman taught last week.
  14. 14. He said that we should use this formula in solving it.
  15. 15. First, determine y2, y1, x2 and x1 in (- 7,18), (-10, -12) then place the values in to get m or the slope.
  16. 16. In(-7,18), (-10,-12) y2 and y1 is the y- coordinates of the second and first ordered pairs respectively, which are -12 and 18.
  17. 17. And the x2 and x1 are the x- coordinates of the second and first ordered pairs respectively, which are -10 and 7.
  18. 18. That’s it! Therefore, the slope is 10!
  19. 19. That means I should take 10 steps from my room, 53O east of south.
  20. 20. From the room, take 10 steps to the southeast!
  21. 21. Here it is! Another love letter from my dear best friend. Oh! How sweet of him!
  22. 22. Congrats Pussy! You’ve got the first clue. So now is the time for the next one. Here’s a graph of a linear equation. Its rise and run will tell the number of steps you’ll take from here. Good luck!
  23. 23. (Click the paw print to return to Garfield)
  24. 24. Uhhh… A graph?! It’s more difficult than the first task. But I’m pretty sure I can solve this.
  25. 25. The length of those broken lines is equal to the steps I’ll take. It is also the rise and the run or the slope.
  26. 26. To get the slope, I need to determine two points on the line. And by observation, we can see that (-7,5) and (0,7) are on the line.
  27. 27. We now have two points and we can solve the rise and run. The slope is also known as the rise over run so the rise is 5 and run is 14. -
  28. 28. That means I have to take 14 steps to the South (because of the negative sign) and 5 steps to the east. But due to the house’s design, I need to take the eastward steps first.
  29. 29. 5 steps to the East then 14 steps to the south.
  30. 30. Oh yeah! I’m so close to finding Pooky. Let’s read Odie’s last love letter for me.
  31. 31. Great job, little pussy. You have done the first two clues and now here’s the last clue. Consider the linear equation below. Its slope is the number of eastward steps you’ll take from here. I’M WISHING YOU A LOT OF LUCK! (Click the paw print to return to Garfield) 0=-16X+2Y
  32. 32. This is an easy one! In an equation, we can solve for the slope by using –a/b! Piece of cake!
  33. 33. In the equation 0=- 16X+2Y, -16 is A and 2 is B. By using –A/B, we get 8 as the slope. Eureka!
  34. 34. Which means 8 steps to the east!
  35. 35. Garfield has reached the place where Odie is waiting. Hey Odie! I’ve solved all of your challenges. Enough already! Where’s Pooky? Alright! Chill! You know that I was just messing with you. You’re good. Since you have solved all my challenges, here, take your Pooky back.
  36. 36. Click to retrieve Pooky
  37. 37. Kids, let me discuss SLOPE OF A LINEAR FUNCTION
  38. 38. In mathematics, the slope or gradient of a line describes its steepness, incline, or grade.
  39. 39. It is the constant rate of change of a linear function.
  40. 40. It can be though of as the ratio of the vertical change to the horizontal change between two points on the graph of a line.
  41. 41. If the two points are (x1, y1) and (x2, y2), then the vertical change is y2 - y1 and the horizontal change is x2 - x1.
  42. 42. Hence, we use the formula
  43. 43. Graph of f(x) = mx + b Positive Slope (the line rises from left to right)
  44. 44. Graph of f(x) = -mx + b Negative Slope (the line falls from left to right)
  45. 45. Graph of f(x) = b Zero Slope (horizontal line; passes through the y-axis)
  46. 46. SUBMITTED TO: Mr. Eric De Guzman Credits to the maker of Garfield the Movie and Garfield Comics

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