2.2 Slope and Rate of Change

Algebra 2Mrs. SpitzFall 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):

run

rise

changeinx

changeiny

xx

yym

12

12

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

5

4

32

4

)3(2

51

m

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)

12

2

2

46

31

)4(6

m

0

6

0

15

22

)1(5

m

Undefined:The line isvertical

m>0, the line rises

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)

22

4

42

731

mline

5

3

5

3

41

522

mline

Since the lines have positive slope & m1>m2 line 1 is steeper