2.2 Slope & Rate of Change
slope
lope:: a numerical value that represents the steepness of a line (m)
m=
vertical change
y − y 1 ∆y rise
= 2
=
=
horizontal change x 2 − x 1 ∆x run
Ex:
Ex: Find the slope of the line containing points (– 2, – 4) and (3, – 1)
***
***NOTE: The larger the value of m, the steeper the slope of the line.
Graphs of Slopes
Ex:
Ex: Find the slope of the line passing through the points and tell whether it rises,
falls, is horizontal, or vertical.
a.) (4, 2) and (– 18, 1)
b.) (– 7, 3) and (– 2, 3)
c.)
1

3

 , −1 and  , −2 
5

5

Parallel vs.
vs. Perpendicular Lines
Ex:
m=
2
3
m =3
m = −1
m =0
m // =
m // =
m // =
m // =
m⊥ =
m⊥ =
m⊥ =
m⊥ =
Ex:
Ex: Determine whether the lines joining the pairs of points are parallel,
perpendicular, or neither.
a.) line 1: (3, 6) and (2, – 1)
line 2: (– 1, 2) and (6, 1)
b.) line 1: (2, – 2) and (– 2, 7)
line 2: (4, – 5) and (5, 1)
Ex: Estimate the slope of each line shown.
ma =
mb =
mc =
md =
Slope as a Rate of Change
In the Mojave Desert in California, temperatures can drop quickly from day to night.
Suppose the temperature drops from 100°F at 2 PM to 68°F at 5 AM. Find the
average rate of change and use it to determine the temperature at 10 PM.
Average rate of change = change in temperature
change in time