Slope

1
Lesson 5-1

• Slope
• or
• Rates of Change

2
Transparency 1
Click the mouse button or press the Space Bar to
display the answers.
3
Transparency 1a
4
Objectives

• Find the slope of a line
• Use rate of change to solve problems

5
Vocabulary

• Slope The ratio of the change in the
  y-coordinates (rise) to the corresponding change
  in the x-coordinates (run) as you move from one
  point to another along a line
• Rate of change How a quantity is changing over
  time

6
x-y Coordinate Plane
Slope, m (?y / ?x)
Point Plotting
5 m ------ -3
up 7
left 4
?y 15
rise
right 5
down 8
run
?x -9
(x, y) (-4, 7) (5, -8) rise ?y
change in y (7 - -8 15) run ?x change in x
(-4 5 -9)
(x, y) (-4, 7) (5, -8) x left or
right y up or down
7
Example 1
Find the slope of the line that passes through
(3, 2) and (5, 5).
8
Example 2
Find the slope of the line that passes through
(3, 4) and (2, 8).
Answer The slope is 4.
9
Example 3
Find the slope of the line that passes through
(3, 4) and (4, 4).
Answer The slope is 0. (A horizontal line!)
10
Example 4
Find the slope of the line that passes through
(2, 4) and (2, 3).
Answer Since division by zero is undefined, the
slope is undefined. (A vertical line!)
11
Example 5
Find the value of r so that the line through (6,
3) and(r, 2) has a slope of ½
12
Example 6
Travel The graph to the right shows the number
of U.S. passports issued in 1991, 1995, and
1999. Find the rates of change for 1991-1995 and
1995-1999.
Use the formula for slope.
13
Example 6 cont
1991-1995
Answer The number of passports issued increased
by 1.9 million in a 4-year period for a rate of
change of 475,000 per year.
14
Example 6 cont
1995-1999
Answer Over this 4-year period, the number of
U.S. passports issued increased by 1.4 million
for a rate of change of 350,000 per year.
15
Summary Homework

• Summary
• The slope of a nonvertical line is the ratio of
  the rise (the change in y) to the run (the change
  in x).
• Homework
• Pg. 260 16-46 even
• Pg. 831 1-13 all