1. 2.5 Model Direct Variation

2. In this lesson you will:
Write direct variation equations.

3. Two variables show direct variation provided y=kx and k is not 0.
K is called the constant of variation and y is said to vary directly with x. The graph of y = kx is a line through the origin.
The variables x and y at the right vary directly, and y=12 when x=4.
Write an equation relating x and y.
Find y when x is 5.
(5,15)
(4,12)
Note: In direct variation the ratio y/x is constant.

4. Does the data show a direct variation between x and y?
This data shows information about 14-karat Gold Chains (1 gram per inch)
Length, x (inches) 16 18 20 24 30
Price, y (dollars)
288
324
360
432
540
Does the data show a direct variation between x and y?
To decide if there is a direct variation, check whether the quotient of y and x is constant.
Yes, the data shows direct variation and the direct variation equation is y = 18x.

5. Does the data show direct variation?
Loose Diamonds (round, colorless, very small flaws)
Weight, x (carats)
0.5
0.7
1.0
1.5
2.0
Price, y (dollars)
2250
3430
6400
11,000
20,400
Does the data show direct variation?