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Slopes (or steepness ) of lines are seen everywhere.

Slopes (or steepness ) of lines are seen everywhere. The steepness of the roof of a house is referred to as the pitch of the roof by home builders. Give one reason why some homes have roofs which have a greater pitch. There is less snow build up in the wintertime.

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Slopes (or steepness ) of lines are seen everywhere.

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  1. Slopes (or steepness) of lines are seen everywhere.

  2. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

  3. Give one reason why some homes have roofs which have a greater pitch. There is less snow build up in the wintertime.

  4. Engineers refer to the slope of a road as the grade.

  5. They often refer to the slope as a percentage.

  6. Slopes and Lines rise run The slope of a line is the steepnessof the line.

  7. 8 100 A grade of 8% would mean for every run of 100 units, there is a rise of 8 units. = 8%

  8. The steepness of wheelchair ramps is of great importance to handicapped persons. 1 12 The slope of wheelchair ramps is usually about If the rise is 1.5 m, what is the run? Ans: 18 m

  9. Determine the slope of the line. 5 cm 9 cm We use the letter m because in French the word for “to go up” is monter. Because the slope is a ratio, there are no units such as cm or cm2.

  10. Determine the slope (pitch) of the roof. 5 m 3 m

  11. Determine the slope of the staircase. 2 3 3 3

  12. 9 3 Determine the slope. 12 10 8 6 4 2 0 2 4 8 6 10 14 12

  13. – 5 7 Determine the slope. 12 10 8 6 4 2 12 0 4 8 6 10 14 2

  14. 7 Determine the slope. 12 10 8 6 4 2 Horizontal lines have a slope of zero. 0 2 4 8 6 10 14 12

  15. 6 Determine the slope. 12 10 8 6 4 Vertical lines have no slope. 2 0 2 4 8 6 10 14 12

  16. negative positive undefined zero Summary: Types of Slopes

  17. Determine the slope of this line. Which points will you use to determine rise and run? 40 5 = 8

  18. Determine the slope of the line segment. –2 60

  19. Draw a line which has a slope of Draw a line which has a slope of 2

  20. Draw a line which has a slope of –5 6 –5 6

  21. Draw a line which has a slope of… b) 3 a) – 3 1 –3 3 1 1 –3 3 1

  22. 9 3 Remember this example? 12 10 8 6 4 2 0 2 4 8 6 10 14 12

  23. You can use the coordinates of two points on the line to find the slope. 12 10 8 6 4 2 0 2 4 8 6 10 14 12

  24. Formula for Slope When given the coordinates of two points on the line: and the slope is the difference of the y-coordinates divided by the difference of the x-coordinates. To represent the difference, we use the Greek letter for d, delta, in the formula. Slope = =

  25. Summary Slope = = =

  26. Examples: Find the slope of the line passing through the two points. Use your answer to decide whether the line is increasing, decreasing, vertical, or horizontal. a) and b) and c) and

  27. Answers: a) decreasing b) vertical c) horizontal

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