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