1. 2.2 SLOPE AND RATE OF CHANGE Algebra 2

2. Warm-up

3. Learning Targets Students should be able to…  Find slopes of lines.  Classify parallel and perpendicular lines.  Use slope to solve real – life problems.

4. Homework Check Section 2.1 Page 71 – 72 #19 – 20, 22 – 23, 25 – 28, 30 – 32, 34, 36, 44, 45

5. Slope Notes The slope of a nonvertical line is the ratio of vertical change (the rise) to horizontal change (the run). The slope of a line is represented by the letter m. Just as two points determine a line, two points are all that is needed to determine a line’s slope. The slope of a line is the same regardless of which two points are used.

6. Slope Notes The slope of the nonvertical line passing through the points (x 1, y 1 ) and (x 2, y 2 ) is:

7. Example 1: Find the slope of the line passing through the points (–2, –4) and (3, –1).

8. Classification of Lines by Slope *A line with a positive slope rises from left to right. (m > 0) *A line with a negative slope falls from left to right. (m < 0) *A line with a slope of zero is horizontal. (m = 0) *A line with an undefined slope is vertical. (m is undefined)

9. Example 2: Without graphing tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. (–2, 3), (1, 5) b. (1, –2), (3, –2)

10. Comparing Slope For two lines with positive slopes, the line with the greater slope is steeper. For two lines with a negative slope, the line with the slope of greater absolute value is steeper.

11. Example 3: Tell which line is steeper. Line 1: through (1, -4) and (5, 2) Line 2: through (-2, -5) and (1, -2)

12. Parallel and Perpendicular Lines

14. Example 4: Tell whether the lines are parallel, perpendicular, or neither. a. Line 1: through (1, –2) and (3, –2) Line 2: through (–5, 4) and (0, 4) b. Line 1: through (–2, –2) and (4, 1) Line 2: through (–3, –3) and (1, 5)

15. Example 5: The slope of a road, or grade, is usually expressed as a percent. For example, if a road has a grade of 3%, it rises 3 feet for every 100 feet of horizontal distance. a) Find the grade of a road that rises 75 feet over a horizontal distance of 2000 feet. b) Find the horizontal length x of a road that has a grade of 4% if the road rises 50 feet over its length.

16. Example 5: The number of U.S. cell phone subscribers increased from 16 million in 1993 to 44 million in 1996. Find the average rate of change and use it to estimate the number of subscribers in 1997.

17. Closure

18. Homework Page 79 – 80 # 17 – 19, 26 – 34 even, 38, 40, 41, 42, 44