Download presentation
Presentation is loading. Please wait.
Published byEsther Pearson Modified over 9 years ago
1
Find Slope and Rate of Change Chapter 2.2
2
How Fast is He Walking? 2
3
3
4
4
5
Rate of Change In this second animation, the man’s speed is itself changing after every second passes The first animation is an example of a constant rate of change In a motor vehicle, you experience a constant rate of change (change of position over time) when the value on your speedometer is not changing The second animation is an example of a variable rate of change In a motor vehicle, you experience a variable rate of change occurs the value on a speedometer changes as time passes 5
6
Rate of Change The graph of two related quantities (like distance and time when something is moving) will be a line if the rate of change is constant This rate of change is commonly called the slope of the line It turns out that the graph of two related quantities, like distance and time, is curved when the rate of change is not constant Such a graph also has a kind of slope; finding this “slope” is the object of one of the two major branches of calculus 6
7
Rate of Change 7
8
Slope of a Line 8
9
9
10
10
11
Example 11
12
Example 12
13
Guided Practice 13
14
Guided Practice 14
15
Classifying Lines by Slope You should be able to tell by looking at a line whether its slope is positive, negative, zero, or undefined Vertical lines have undefined slopes because, using the slope formula, the denominator yields zero and division by zero is not defined Horizontal lines have zero slopes because, using the slope formula, the numerator yields zero and every non-zero number divided by zero is zero For the last two cases, imagine that you are walking on a line from left to right in the coordinate plane 15
16
Negative Slope 16
17
Negative Slope 17
18
Positive Slope 18
19
Positive Slope 19
20
Classification of Line by Slope A vertical line has an undefined slope A horizontal line has a slope of zero A line that falls from left to right has a negative slope A line that rises from left to right has a positive slope 20
21
Example 21
22
Guided Practice 22
23
Guided Practice 23
24
Parallel & Perpendicular Lines Recall from geometry that Two lines are parallel if they never intersect Two lines are perpendicular if they intersect at right angles (90˚) It is possible to show how the slopes of lines that are parallel or lines that are perpendicular are related, but this is lengthy so we will just remember the relationship 24
25
Parallel & Perpendicular Lines Two non-vertical lines are parallel if and only if their slopes are equal The phrase “if and only if” means two things: Two lines are parallel if their slopes are equal Two lines with equal slopes are parallel 25
26
Parallel & Perpendicular Lines 26
27
Example 27
28
Example 28
29
Example 29
30
Guided Practice 30
31
Guided Practice 31
32
Guided Practice 32
33
Rate of Change At the beginning of this presentation, we considered slope as the ratio of the change in the distance a man walked compared to the time that passed The slope of a line is always the ratio of the change in one quantity compared to the change in another That is, slope is an average rate of change 33
34
Example 34
35
Guided Practice A Giant Sequoia tree has a diameter of 248 inches in 1965 and a diameter of 251 inches in 2005. Find the average rate of change in the diameter. Include units in your answer. 35
36
Guided Practice 36
37
Exercise 2.1 Handout 37
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.