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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.
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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):
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