5.1 Rate of Change and
Slope
Objective: SWBAT determine the
slope of a line given a graph or two
ordered pairs.
Mini Quiz 39
1. Find the domain and range of the function:
2. What is the greatest value in the range of y=2x+4 for
the domain {-2, -1, 0, 1}
Quick Preview
The diagram at the right shows the
side view of a ski lift.
1. What is the vertical change from:
a. A to B?
10 feet
b. B to C?
40 feet
c. C to D?
10 feet
2. What is the horizontal change from:
a. A to B? 30 feet
3. Find the ratio of the vertical change to the
b. B to C? 30 feet horizontal change for each section of the ski
lift.
c. C to D 30 feet
A 1 B 4 C 1
= ;
=
;
=
B 3 C 3 D 3
4. Which section is the steepest? B to C
Rate of Change
change in the dependent variable
Rate of change  change in the independen t variable
What is the rate of change for the data
to the left?
change of dependent = $15
change of independent = 1 day
$15 = $15/day
1 day
What does the rate of change mean?
It cost $15 more to rent a computer
each day.
The Magnum
Cedar Point, OH
Superman
6 Flags Magic
Mountain
Ghost Rider
Knott’s Berry Farm
Xcelerator
Knott’s Berry Farm
How steep is the steepest roller coaster?
Son of Beast
King’s Island, OH
These are
completely
vertical!
Imagine a roller coaster
moving from LEFT to RIGHT
There are four different
kinds of slope the coaster
could encounter...
And 2 Special Cases…
The zero-fun
coaster
The
impossibly
scary
coaster
What
kind of
slope are
they?
Aw!
That’s
zero fun!
That’s a really
scary coaster,
so the slope
is…
For the following slides,
call out whether the slope is
positive, negative, zero, or
undefined.
3
Wait for the count of
before you say your answer!
How do you calculate the slope
of a line?
1. Pick two points on the line
2. Calculate “rise over run”
3. Determine the sign
Start with 2 points on
gridline intersections
How do you calculate the
slope of a line?
m =
Slope
OR...
Vertical change
Horizontal change
Rise
m =
Slope
Run
Run
Rise
What sign is it?
Show me!
Look to see if the slope is
increasing
Or decreasing
Model # 1: Watch me do the
Step 1:three
Choose
2
points
steps
Step 2:
Rise
Slope =
Run
Run = 1
Rise = 2
Step 3:
Determine
the sign
Rise
2+
m=2
Run
1
Model # 2: Watch me do the
Step 1:
Choose
2
points
three steps
Step 2:
Rise
Slope =
Run
Run = 3
Rise = 1
Step 3:
Determine
the sign
Rise
1
m = 1/3
Run
3
Practice # 3: Find the slope of this line
Run = 2
Rise = 3
Rise
Run
m
+3
2
Practice # 4: Find the slope of this line
Run = 3
Rise
Run
Rise = 1
1
m
3
Slope Formula
y2  y1
m
x2  x1
x1
y1
x2 y2
5. Given (5, -3) and (-4, 2), find
the slope of the line.
m = 2  (3)  5
45 9
Slope Formula
y2  y1
m
x2  x1
x1
y1
x2 y2
6. Given (0, -2) and (4, -2), find
the slope of the line.
m =  2  ( 2 )  0  0
40
4
Tell your partner...
What are the steps to find the slope of
a line from a graph?
Calculate
rise over run.
Look at the
line to see if
the slope is
positive or
negative.
Wrap Up
• Rate of Change (includes units)
y2  y1
• Slope rise 
run 
– Positive
– Negative
– Zero
– Undefined
m
x2  x1
HW: P. 234 #1-29 odd, 75-85 odd
DLUQ: What’s the difference between slope
and rate of change?
Before you leave:
1. What type of slope is shown? (Positive, negative,
zero or undefined?)
2. What would a slope of -1/2 look like? (Uphill,
downhill, steep, shallow)
3. What is the slope of the line above?