2 2 Slope and Rate of Change Algebra

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

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

Assignment n pp. 79 -80 #4 -47 all

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

The slope of a line n The slope of a nonvertical line passing thru the points (x 1, y 1) (x 2, y 2):

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

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

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

n 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 n For two lines, the line slope of greater absolute value is steeper.

Tell which line is steeper n n Line 1 thru (2, 3) & (4, 7) or Line 2 thru (-1, 2) & (4, 5) Since the lines have positive slope & m 1>m 2 line 1 is steeper