5.5 Direct Variation
As you watch a movie, 24 individual pictures, or frames, flash on the screen each second.
Here are three ways you can model the relationship between the number of frames and the number of seconds.
3
4
1
2
5
Table x y
(sec) (frames)
24
48
72
96
120
120
80
40
Graph
1 2 3 4 5
Function Rule y = 24x
Questions:
1. What is the rate of change for the data in the table?
2. What is the slope of the line shown in the graph?
3. What is the relationship between the rate of change, the slope, and the coefficient of x in the function rule?

**The number of frames varies directly with the number of seconds the movie has been shown.
This relationship is called a direct variation.
Definition: A direct variation is a linear function that can be written in the form y = k x where k = 0 constant of variation
**The graph of a direct variation will always pass through the origin!

Does the equation represent a direct variation?
If so, what is the constant of variation ?
y = 7x y = 4x - 10
5x - 2y = 0
-8y = 24x x + y = 7

Tell whether the relationship is a direct variation.
15
20 x y
10 2
3
4 x y
4 8 12
16 20 24 x y
-3 -6 -9
18 36 54 x 8 0 -5 y 13 5 0

Examples:
The variables x and y vary directly.
When x = 5, y = 20.
Write an equation that relates x and y
Now find the value of y when x = 20

The time it takes you to hear thunder varies directly with your distance from the lightning.
If you are 2 miles from where lightning strikes, you will hear thunder about 10 seconds after you see the lightning.
Write an equation showing the relationship between time and distance.

The amount of money you get paid varies directly with the number of hours you work.
When you work 17 hours, you get paid $80.41.
Write a direct variation equation that relates your pay and the number of hours you work.
Now find your pay when you work 20 hours.
Now find the number of hours you need to work to get paid $137.17