2.1-2.4 Quiz on
Monday!
2.4: More On Slope
Parallel and Perpendicular Lines
 Two distinct lines are parallel if and only if
o they have the same slope.
o or they both have an undefined slope.
 Two lines are perpendicular if and only if
o Their slopes are opposite reciprocals (the
product of their slopes is -1).
o or the slope of one line is 0 and the slope
of the other is undefined.
1. Write the equation of the line described in slope-intercept form.
a. Passing through (3, −8) and parallel to the line 12𝑥 − 3𝑦 =
100.
b. Passing though (2, 3) and perpendicular to the line
12𝑥 + 16𝑦 = 20.
Slope as a rate of change
Slope, as we know, tells us the rate of change of a function.
Describe a rate of change in the following table?
Time eating
(minutes)
0
1
2
3
Amount of
Cheetos in the
bag
200
176
152
128
 Linear functions are the only functions with a constant rate of
change.
 However, we can discuss rates of change on any function.
1
2. Find the average rate of change of the function 𝑓(𝑥 ) = 𝑥 2 + 3
2
a. From 0 𝑡𝑜 2
b. From 2 𝑡𝑜 4
3
3. Find the average rate of change of the function 𝑓(𝑥 ) = 2 √𝑥 − 8
a. From 0 𝑡𝑜 1
b. From 0 𝑡𝑜 27
4. A certain population of bacteria (in thousands) in Mr. Muzny’s
shoe can be modeled by the function
𝑝(𝑡) = 0.055𝑡 2 + 2.8𝑡 + 220
where t represents time (minutes).
a. Find the average rate of change from 𝑡 = 10 to 𝑡 = 20
b. Describe what this means in the context of the problem.
5. The function 𝑓 (𝑡) = 0.5𝑡 3 + 2√𝑡 gives Mr. Cawelti’s position on
his jet ski (in meters) relative to a sunbathing Mr. Propri, where 𝑡
is time (in seconds). What Mr. Cawelti’s average velocity in the
first 5 seconds?
6. The average rate of change of the function 𝑓(𝑥) is -2.4 on the
interval from 𝑥 = −6 to 𝑥 = 18. Find 𝑓(−6) if 𝑓(18) = 30.