1. 2.2 Slope and Rate of Change Algebra 2 Mrs. Spitz Fall 2009

2. Objectives • Find slopes of lines and classify parallel and perpendicular lines. • Use slope to solve problems, such as how to safely adjust a ladder.

3. Assignment • pp. 79-80 #4-47 all

4. The slope of a nonvertical line is the ratio of vertical change (the rise) to the horizontal change (the run). • The slope of a line is represented by the letter m. • Just like any 2 points determine a line, any 2 points are all that are needed to determine the slope. • The slope of the line is the same regardless of which 2 points are used

5. The slope of a line • The slope of a nonvertical line passing thru the points (x1,y1) (x2,y2):

6. Find the slope of a line passing thru (-3,5) & (2,1)

7. Classification of lines by slope • A line with positive slope: rises from left to right (m>0) • A line with negative slope: falls from left to right (m<0) • A line with slope of zero is horizontal (m=0) • A line with undefined slope is vertical (m is undefined)

8. W/out graphing, tell whether the line thru the points rises, falls, horizontal, or vertical. • 1) (3,-4), (1,-6) • 2) (2,-1), (2,5) m>0, the line rises Undefined: The line is vertical

9. Not only does slope tell you whether the line rises, falls, is horizontal, or is vertical; it also tells you the steepness of the line • For two lines, the line slope of greater absolute value is steeper.

10. Tell which line is steeper • Line 1 thru (2,3) & (4,7) • or Line 2 thru (-1,2) & (4,5) Since the lines have positive slope & m1>m2 line 1 is steeper