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Slope

Slope. run. rise. Slope =. Slope of a Linear Relationship. The Slope of a linear relationship is the steepness of the line. Slopes are seen everywhere. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

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Slope

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  1. Slope

  2. run rise Slope= Slope of a Linear Relationship The Slope of a linear relationship is the steepnessof the line.

  3. Slopes are seen everywhere.

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

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

  6. Engineers refer to the Slope of a road as the grade.

  7. They often represent the slope as a percentage.

  8. 100 8 Slope = A grade of 8% would mean for every rise of 8 unitsthere is arun of 100 units. = 8%

  9. The steepness of wheelchair ramps is of great importance for safety. 1 12 Slope of wheelchair ramp = If the rise is 1.5 m, what is the run? Answer: 18 m because

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

  11. 3 2 3 3 Determine the rate of change of each staircase.

  12. Determine the Slope. Which points will you use to determine rise and run? Earnings 4 20 = $5/hr What does this rate of change represent? Number of Hours Worked The hourly wage

  13. POSITIVE SLOPES • Goes up to the right

  14. Negative Slope • Goes down to the right

  15. STEEPNESS OF SLOPE • The greater the _ Constant of variation_(steapness)__, the ___Greater__ the slope! • (i.e. a slope of -10 is __Greater_______ than a slope of 8) • A ski hill has two runs with a slope of 6% and 10%. Represent their slopes in a graph.

  16. HOW DO WE MEASURE SLOPE? • Slope compares the __Rise__ to the run__ to determine the __Slope______ steepness • Slope can be represented by the letter __m___ • The formula for slope is given by: • Slope = Rise/Run

  17. Try it • A ski jump is 90 metres high and takes up a horizontal distance of 32 metres along the ground. What is the slope of the jump?

  18. Try these

  19. Answers • Slope =-5/2 2/3 3/1 =3

  20. Lets apply this stuff • A line segment has an endpoint at (5, 4) and a slope of -2/3. Find another point on the line. • Using a graph: • therefore (8,2) • Using the coordinates:

  21. Using coordinates • A line segment has an endpoint at (5, 4) and a slope of -2/3. Find another point on the line. • 5+3=8 • 4-2 = 2 therefore (8,2)

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