1. Algebra
Direct Variation

2. Do Now

3. Direct Variation Model
The two variables x and y are said to
vary directly if their relationship is:
y = kx
k is the same as m (slope) k is called the constant of variation

4. The price of hot dogs varies directly with the number of hotdogs you buy
You buy hotdogs.
x represents the number of hotdogs you buy.
y represents the price you pay.
y = kx Let’s figure out k, the price per hotdog.
Suppose that when you buy 7 hotdogs, it costs $21.
Plug that information into the model to solve for k.
y = kx
21 = k(7) Now divide both sides by 7
to solve for k.
k = 3 The price per hotdog is $3.
y = 3x You could use this model to find the price (y) for any number of hotdogs (x) you buy.

5. goes through the origin.y
The graph of y = 3x
goes through the origin. x
All direct variation graphs go through the origin, because when x = 0, y= 0 also.

6. . . . . y (price) y = 3x (3,9) When you buy 3 hotdogs, you pay $9
(1,3) When you buy 1 hotdog, you pay $3 .
x (number of hotdogs)
(0,0) When you buy 0 hotdogs, you pay $0

7. Finding the Constant of Variation (k)
STEPS
Plug in the known values for x and y into the model: y = kx
Solve for k
Now write the model y = kx and replace k with the number
Use the model to find y for other values of x if needed

8. Example The variables x and y vary directly. When x = 24, y = 84.
Write the direct variation model that relates x and y.
Find y when x is 10.

9. Example The variables x and y vary directly. When x = 24, y = 84.
Write the direct variation model that relates x and y.
Find y when x is 10. 1.

10. Example The variables x and y vary directly. When x = 24, y = 84.
Write the direct variation model that relates x and y.
Find y when x is 10. 1.

11. Example The variables x and y vary directly. When x = 24, y = 84.
Write the direct variation model that relates x and y.
Find y when x is 10. 1.

12. Example The variables x and y vary directly. When x = 24, y = 84.
Write the direct variation model that relates x and y.
Find y when x is 10. 1. 2.

13. Example The variables x and y vary directly. When x = 24, y = 84.
Write the direct variation model that relates x and y.
Find y when x is 10. 1. 2.
When x = 10, y = 35

14. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5.

15. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5. 1.

16. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5. 1.

17. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5. 1.

18. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5. 1.

19. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5. 1. 2.

20. Example The variables x and y vary directly. When x = ½, y = 18.
Write the direct variation model that relates x and y.
Find y when x is 5. 1. 2.
When x = 5, y = 180

21. Work Rookie-Pg. 302 # 9,11 Veteran-Pg. 302 # 15, 17
All Star-Pg. 302 # 21,25