1. RATE OF CHANGE AND DIRECT VARIATION
SECTION 5.3

2. 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

3. Example 1: Find the speed (rate of change) for each object.
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 40 60 80
100
120
Time (minutes)

4. Example 1: Find the speed (rate of change) for each object.
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
1.0
1.5
2.0
2.5
3.0
Time (hours)

5. 16.7 feet per second 50 feet 3 seconds 3 50 100 80 60 Distance (feet)40 20
16.7 feet per second 1 2 3 4 5 6
Time (seconds)

6. 187.5 miles per day 750 miles 4 days 4 750 2500 2000 1500
Distance (miles)
750
1000
187.5 miles per day
500 4 8 12 16 20 24
Time (days)

7. The student walked forward 5 feet in 3 seconds.
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. 10
He then walked backwards 3 feet in 2 seconds. 8
He stood still for 1 second. 6
Distance (feet)
He then walked forward 2 feet in 3 seconds. 4 2 2 4 6 8 10 12
Time (seconds)

8. One type of rate of change is ______________. direct variation
If y varies directly as x, then ____________, or _____________,
where k is the constant of variation.

9. Example 2: Looking For the Constant of Variation (k)
A. If y varies directly as x and
when
, find the constant of variation
and write the equation for direct variation.

10. B. If y varies directly as x and , find the constant of variation
when
, find the constant of variation
and write the equation for direct variation.

11. If y varies directly as x and , find the constant of variation
when
, find the constant of variation
and write the equation for direct variation.

12. Example 3: Looking For the missing value of x or y.
A. If y varies directly as x and
when
, find x when
You can set up and solve a proportion to find x or y. .

13. A. If y varies directly as x and , find y when

14. If y varies directly as x and , find x when.