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.

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):
y2  y1 changeiny rise
m


x2  x1 changeinx run
Find the slope of a line
passing thru (-3,5) & (2,1)
1 5
4 4
m


2  (3) 2  3 5
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)
m>0, the line rises
 6  (4)  6  4  2
m


1
1 3
2
2
Undefined:
 2) (2,-1), (2,5)
The line is
5  (1) 5  1 6
m

 vertical
22
0
0
 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)
37  4
line1m 

2
24 2

or Line 2 thru (-1,2) & (4,5)
25
3 3
line 2m 


1  4  5 5
Since the lines have positive slope &
m1>m2 line 1 is steeper