Chapter 2.2Slope & Rate-of-Change
#8 A mathematician is a scientist who can figure out anything except such simple things as squaring the
circle and trisecting an angle. ~Evan Esar, Esar's Comic Dictionary#9 Math is radical! ~Bumper
Sticker
p86 3-11, 18-23, 25,26, 41
Slope
The ratio of the vertical change of a line to the horizontal change. Rise over run.
y
mx
Run
Ris
e
2
5m
2 1
2 1
y y
x x
Rise
Run
Find slope
Through (15,8) & (3,-2) 2 1
2 1
y y
mx x
Find slope
Through (15,8) & (3,8)2 1
2 1
y y
mx x
Types of Slopes
Positive Slope Negative Slope
0m 0m
HOY VUX
• H - horizontal
• O - M=0
• Y - Y=(some number)
• V - Vertical
• U - M=Undefined
• X - X=(some number)
HOY VUX
Zero Slope Undefined Slope
0m .m und
examples
examples
examples
Parallel & Perpendicular
• Parallel – Lines that never cross. Have the same slopes
• Perpendicular – Lines intersect at one point. Slopes are negative reciprocals of each other.
examples
• Parallel
examples
• Perpendicular
Are each set of lines parallel, perpendicular or neither?
Line 1: Through (15,8) & (3,-2)
Line 2: Through (-3,6) & (-9,1)2 1
2 1
y y
mx x
1
8 2
15 3m
2
6 1
3 9m
10 12
5
6
5 6
Are each set of lines parallel, perpendicular or neither?
Line 1: Through (5,6) & (-2,2)
Line 2: Through (-3,3) & (-7,10)2 1
2 1
y y
mx x
1
6 2 5 2
m
2
3 10
3 7m
4 7
7
4
Are each set of lines parallel, perpendicular or neither?
Line 1: Through (5,4) & (2,2)
Line 2: Through (-6,8) & (9,10)2 1
2 1
y y
mx x
Rate-of-Change
• Rate-of-Change – To calculate a rate of change just find the slope of the values.
• Units – Expressed as the ratio of the units of the y-value over the units of the x-value.
ExampleIf the population of a city changed from 5,000 people in 1990 to 3,000 people in 2000 what was the rate-of-population
change for the city?
x valuey value
yearpopulation
2 1
2 1
y y
mx x
3000 5000
2000 1990
2000
10
-200 people
year
Assignment
• p86 3-11, 18-23, 25,26, 41
