3-4 rate of change and slope
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3-4 Rate of Change and Slope. Objective: SWBAT determine the slope of a line given a graph or two ordered pairs. Mini Quiz 39. 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. - PowerPoint PPT PresentationTRANSCRIPT
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3-4 Rate of Change and Slope
Objective: SWBAT determine the slope of a line given a
graph or two ordered pairs.
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Mini Quiz 391. 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}
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Quick PreviewThe diagram at the right shows the
side view of a ski lift.
1. What is the vertical change from:
a. A to B?
b. B to C?
c. C to D?
2. What is the horizontal change from:
a. A to B?
b. B to C?
c. C to D
3. Find the ratio of the vertical change to the horizontal change for each section of the ski lift.
4. Which section is the steepest?
10 feet
40 feet
10 feet
30 feet
30 feet
30 feet A 1 B 4 C 1B 3 C 3 D 3
= ; = ; =
B to C
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Rate of Change
change of Rate variabledependent in the change
t variableindependen in the change
What is the rate of change for the data to the left?
change of dependent = $15change 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.
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The MagnumCedar Point, OH
Ghost RiderKnott’s Berry
FarmXcelerator
Knott’s Berry Farm
Superman6 Flags Magic
Mountain
Son of BeastKing’s Island, OH
How steep is the steepest roller coaster?
These arecompletely
vertical!
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Imagine a roller coaster moving from LEFT to RIGHT
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There are four different kinds of slope the coaster
could encounter...
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And 2 Special Cases…
The zero-fun coaster
The impossibly
scary coaster
What kind of slope are
they?
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Aw!That’s zero fun!
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That’s a really scary coaster, so the slope
is…
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For the following slides,call out whether the slope is positive, negative, zero,
or undefined.
Wait for the count of 3 before you say your
answer!
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negative
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posit
ive
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zero
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und
efined
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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
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Start with 2 points on gridline intersections
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How do you calculate the slope of a line?
Slope =
Vertical change
Horizontal change
OR... RiseRun
m
Slope =m
Rise
Run
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What sign is it?
Look to see if the slope is increasing
Or decreasing
Show me!
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Model # 1: Watch me do the three stepsStep 1: Choose 2 points
Rise = 2
Run = 1
RiseRun21
m = 2
Step 3:Determine
the sign
posi
tive
Slope =
RiseRun
Step 2:
+
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Model # 2: Watch me do the three stepsStep 1: Choose 2 points
Rise = 1
Run = 3
RiseRun13
m = 1/3
Step 3:Determine
the sign
negative
Slope =
RiseRun
Step 2:
-
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Practice # 3: Find the slope of this line
RiseRun
Rise = 3
Run = 2
23
m+
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Practice # 4: Find the slope of this line
Rise = 1
Run = 3
31
m
RiseRun
negative
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Slope Formula
12
12
xx
yym
5. Given (5, -3) and (-4, 2), find the slope of the line.
x1 y1 x2 y2
m =54
)3(2
9
5
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Slope Formula
12
12
xx
yym
6. Given (0, -2) and (4, -2), find the slope of the line.
x1 y1 x2 y2
m =04
)2(2
4
0 0
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Tell your partner...What are the steps to find the slope
of a line from a graph?
Calculaterise over run.
Look at theline to see ifthe slope is positive ornegative.
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Wrap Up• Rate of Change (includes units)• Slope
– Positive– Negative– Zero– Undefined
HW: P. 234 #1-29 odd, 75-85 odd
DLUQ: What’s the difference between slope and rate of change?
run
rise
12
12
xx
yym
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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?