2.2 Slope and Rate of Change
Algebra 2
Learning Targets
I can find slopes of lines and classify parallel and perpendicular lines.
I can use slope to solve real-life problems.
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
Two lines are parallel if they don’t intersect.
Two lines are perpendicular if they intersect to form a right angle.
Parallel and Perpendicular Lines
Slope can be used to determine if 2 lines are װ or ┴
Parallel Lines lines m1 = m2 (the slopes are =) װ
Perpendicular Lines ┴ lines (negative
reciprocals)2
1
1
mm
Tell whether the lines are or neither ,┴,װ
L1: thru (-3,3) & (3,-1)
L2: thru (-2,-3) & (2,3)
3
2
6
4
33
4
)3(3
3111
ml
2
3
4
6
22
33
)2(2
)3(322
ml
Negative reciprocalsOf each other :They are ┴.
Using slope. Turn to p. 78 ladder problem.1. Max recommended slope
m=12/3=42. X=min distance from wall to
reach 20’ Write a proportion
The rise is 20, the run is X Cross multiply and solve X=5 The ladder’s base
should be 5’ from the wall
12
3
20
X
X
20
1
4
Pair-share
Work on 2.2 Practice B classwork.
Homework
pp. 79-80 #4-47 all
Resources:
Modified from the website below: http://www.taosschools.org/ths/Depart
ments/MathDept/spitz/Courses/Algebra2/presentations.htm