RATE OF CHANGE AND DIRECT VARIATION

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RATE OF CHANGE AND DIRECT VARIATION
SECTION 5.3
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VERTICAL AXIS
HORIZONTAL AXIS
HORIZONTAL CHANGE
VERTICAL AXIS
VERTICAL CHANGE
HORIZONTAL AXIS
slope
Rate of change is related to the __________ of a
line because they are both a ratio of the change
in ______ over the change in __________.
vertical
horizontal
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The graphs below show the distance that an object
travels at a constant speed. Example 1 Find
the speed (rate of change) for each object.
2000
800miles
80 minutes
1600
1200
80
Distance (miles)
800
800
10 miles per minute
400
20
60
40
80
100
120
Time (minutes)
4
The graphs below show the distance that an object
travels at a constant speed. Example 1 Find
the speed (rate of change) for each object.
200
60 miles
1.0 hours
160
1.0
120
Distance (miles)
60
80
60 miles per hour
40
0.5
1.5
1.0
2.0
2.5
3.0
Time (hours)
5
50 feet
3 seconds
3
100
80
50
60
Distance (feet)
40
20
16.7 feet per second
1
3
2
4
5
6
Time (seconds)
6
750 miles
4 days
2500
2000
4
1500
Distance (miles)
750
1000
187.5 miles per day
500
4
12
8
16
20
24
Time (days)
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The graph below was made from data collected by a
motion detector. In the experiment, a student
walked in a straight line away from the motion
detector. Describe the movement of the person by
identifying the rates of change shown on the
graph below.
The student walked forward 5 feet in 3 seconds.
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He then walked backwards 3 feet in 2 seconds.
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He stood still for 1 second.
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Distance (feet)
He then walked forward 2 feet in 3 seconds.
4
2
2
6
4
8
10
12
Time (seconds)
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One type of rate of change is ______________.
direct variation
If y varies directly as x, then ____________, or
_____________, where k is the constant of
variation.
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Example 2 Looking For the Constant of
Variation (k)
when
, find the constant of variation
A. If y varies directly as x and
and write the equation for direct variation.
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B. If y varies directly as x and
when
, find the constant of variation
and write the equation for direct variation.
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If y varies directly as x and
when
, find the constant of variation
and write the equation for direct variation.
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Example 3 Looking For the missing value of x
or y.
when
, find x when
A. If y varies directly as x and
You can set up and solve a proportion to find x
or y.
.
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when
, find y when
A. If y varies directly as x and
.
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when
, find x when
If y varies directly as x and
.