1. Entry Task – SHOW WORK 34
-107

2. Write and interpret direct variation equations
Target: I can
Write and interpret direct variation equations

3. Another way of writing this is k =
Definition:
Y varies directly as x means that y = kx where k is the constant of variation.
Another way of writing this is k =
In other words:
* the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.

4. When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.

5. Direct variation uses the following formula:

6. Direct Variation example:
if y varies directly as x and y = 10 as x =2.4, find x when y =15. what x and y go together?

7. Direct Variation
If y varies directly as x and y = 10 find x when y =15.
y = 10, x = make these y1 and x1
y = 15, and x = ? make these y2 and x2

8. Direct Variation
if y varies directly as x and y = 10 as x = 2.4, find x when y =15

9. How do we solve this? Cross multiply and set equal.
Direct Variation
How do we solve this? Cross multiply and set equal.

10. Direct Variation We get: 10x = 36
Solve for x by diving both sides by 10.
We get x = 3.6

11. Direct Variation Let’s do another.
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Set up your equation.

12. If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Direct Variation
If y varies directly with x and y = 12 when x = 2, find y when x = 8.

13. Cross multiply: 96 = 2y Solve for y. 48 = y.
Direct Variation
Cross multiply: 96 = 2y
Solve for y = y.

14. Examples of Direct Variation:
Note: X decreases,
10, 5, 3
And Y decreases.
30, 15, 9
What is the constant of variation of the table above?
Since y = kx we can say Therefore:
30/10=k or k = 3 15/5=k or k = 3
9/3=k or k =3 Note k stays constant.
y = 3x is the equation!

15. Y varies directly as x. Find the constant of variation and write an equation for the direct variation when y = 42 when x = 7
Find the value of k.
y=kx Direct variation formula
42 = k(7) Replace y with 15 and x with 5.
42= k(7)
Divide each side by 5
6 = k Simplify
Equation?
y = 6x

16. Tell if the following graph is a Direct Variation or not.
Yes No No No

17. Tell if the following graph is a Direct Variation or not.1. 2.
Yes No 3. 4. No
Yes

18. Using Direct Variation to find unknowns (y = kx)
Given that y varies directly with x, and y = 6 when x=-5,
Find y when x = HOW???
2 step process
1. Find the constant variation.
k = y/x or k = 6/-5 = -1.2
k = -1.2
2. Use y = kx. Find the unknown (x).
y= -1.2(-8)
x= 9.6
Therefore:
X =-8 when Y=9.6

19. Using Direct Variation to solve word problems
A car uses 8 gallons of gasoline to travel 290 miles. How much gasoline will the car use to travel 400 miles?
Step One: Find points in table
Step Three: Use the equation
to find the unknown.
400 =36.25x
or x = 11.03
Step Two: Find the constant variation and equation:
k = y/x or k = 290/8 or 36.25
y = x

20. Homework
P. 71 # 7-47 odds
Challenge - # 54