1. Slope

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

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

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

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

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

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