1. Chapter 2.2 Slope and Rate of Change

2. Things to know from Chapter 2.2 1.) How to calculate slope from 2 points. 2.) Determine rise, fall, horizontal, and vertical slopes. 3.) Determine the steeper line based on slopes. 4.) Determine whether lines are parallel, perpendicular or neither.

3. Slope can be expressed different ways: A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right.

4. Rates of change are seen everywhere.

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

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

7. 3 m 5 m Determine the rate of change (pitch) of the roof.

8. Engineers refer to the rate of change of a road as the grade.

9. They often represent the rate of change as a percentage.

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

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

12. Determine the rate of change. 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

14. ** Roof requirement must rise 3ft. for every 15 ft. of horizontal distance. a. What is the required pitch or slope of the roof? b. What is the minimum required height of the roof? c. Use the Pythagorean Theorem to determine the length of one side of the roof. 130 ft h rise run 3 15 1 5 1 5 h 65 = h = 13 13 feet 13 13² + 65² = length² length = 66.3 feet

16. Work Pg. 80 48-52