7th Grade Math

Lesson 3C Variation 407

Identify Direct Variation

Determine whether each linear function is a direct variation. If so,

state the constant of variation.

(^) Time, x 1234
Wages, y 12 24 36 48
Compare the ratios to check for a common ratio.
wages
time^
^12
1
^24
2
or ^12
1
^36
3
or ^12
1
^48
4
or ^12
1
Since the ratios are the same, the function is a direct variation. The
constant of variation is _^12
1
.
(^) Time (h), x 2345
Temperature Change (°), y 45711
temperaturetime ^4
2
or ^2
1
^5
3
or 1.67
1
^7
4
or 1.75
1
^11
5
or _2.2
1
The ratios are not the same, so the function is not a direct
variation.
c. Year, x 5 101520
Height, y 12.5 25 37.5 50
Linear Functions
Table Graph Equation
Direct
Variation
Functions
xy
y
_x

• 2 - 63


• 1 - 33
  133
  263

y

246 x

6

4

2

• 6 - 4 - 2
  
  
  • 4
  
  
  • 6
  
  
  
  

0

y = 3x

Not Direct

Variation

Functions

xy

y

_x

• 2 - 7 _- 27


• 1 - 44
  122
  25 5 _ 2

y

0 246 x

6

4

2

• 6 - 4 - 2
  
  
  • 4
  
  
  • 6
  
  
  
  

y = 3x - 1

Direct Variation Direct Variation When a

relationship varies directly,

the graph of the function

will always go through

the origin. So, (0, 0) is a

solution of y = 3 x.

404_415_C07_L3_895130.indd 407 12/31/09 4:32 PM