2.2 Slope and Rate of Change

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Presentation transcript:

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

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

Assignment 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). 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

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

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

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)

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

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.

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