1. Advanced Algebra Notes Section 2.2: Find Slope & Rate of Change The steepness of a line is called the lines The slope of a non-vertical line is: The slope of a line is represented by the letter To determine the slope of a line you must know two points on that line. Slope Formula: “Rise over run gets the job done!” slope m zero

2. Example 1 Find the slope of a line passing through (-2, 4) and (-3,-1).

3. Classifying Slopes of Lines 1.A line with a rises from left to right. (m > 0) 2.A line with a falls from left to right. (m < 0) 3.A line with a is horizontal. 4.A line with a (no slope) is vertical. ( m is undefined) We always go left to right! negative slope zero slope undefined slope positive slope

4. Without graphing, tell whether the line through the given point rises, falls, is horizontal or is vertical. A.(-2, 3) and (1, 5) B.(1,-2) and (3, -2) Rises

5. The slope of the lines can also tell you which line is steeper. If two lines have a, the line with the. whole number slope greater numerator will be steeper greater fraction will be steeper fraction as a slope ½ (or.5) will be steeper than ¼ (or.25)

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

7. Two lines are if they have the same slope. (m 1 = m 2 ) Two lines are if and only if their slopes are opposite reciprocals of each other. parallel perpendicular

8. 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) 0 0 Parallel ½ 2 Neither

9. Slopes can be used to represent an average, or how much one quantity changes relative to the change in another quantity. rate of change

10. Example 5: A water park slide drops 8 feet over a horizontal distance of 24 feet. A.Find its slope B.Find the drop over a 54 foot section with the same slope. 24 ft 8 ft