1. Meg, Emma, Caroline, Laura, Pitzer, Luke
Lesson 4.5
Meg, Emma, Caroline, Laura, Pitzer, Luke

2. Video

3. Direct Variation Notes
Direct Variation- special type of linear relationship that can be written by the form y=kx
Constant of variation- the k in the equation y=kx is the nonzero constant

4. Examples
directions: tell whether each equation represents a direct variation. If so, identify the constant of variation.
-3x+5y=0
Answer: Y=3/5x = The constant of variation is /5

5. Example 2x+y=10 Not a direct variation y=4x+9 Not a direct variation
2y=-8x y=-4x Constant of Variation:-4

6. Graphing To Graph: 1. Write a direct variation equation.
2. Choose values of x and generate ordered pairs.
3. Graph the points and connect.

7. Example X Y=6x (x,y) Y=6(0)=0 (0,0) 1 Y=6(1)=6 (1,6) 2 Y=6(2)=12
The three-toed sloth is an extremely slow animal. On the ground, it travels at a speed of about 6 feet per minute. Write a direct variation equation for the distance y a sloth will travel in x minutes. They graph. X
Y=6x
(x,y)
Y=6(0)=0
(0,0) 1
Y=6(1)=6
(1,6) 2
Y=6(2)=12
(2,12)

8. Walk-through X 1 3 5 Y 6 18 30 Method 1:
Y=6x: each y-value is six times the corresponding x-value
Method 2:
Put the pairs into fraction form: y/x
6/1=6, 18/3=6, /5=6

9. Examples
Method1: y=x-4
Method2: -2/2=-1, 0/4=0, 4/8=1/2: not a direct variation
Y=7x X 2 4 8 Y -2
Cameron earns $7 dollars per hour at her after school job. The total amount of her pay checks varies directly with the amount of time she works. Write a direct variation equation for the amount of money y that she earns for working x hours.