Download presentation

Presentation is loading. Please wait.

1
Exercise Solve. 5 = 3x x = 5 3

2
Exercise Solve. 4 = k 1 3 k = 12

3
Exercise Solve. y 25 3 5 = y = 15

4
Exercise Solve. 3 5 25 x = x = 41 2 3

5
Exercise If 4 = 6k, what is the value of 3k? 2

6
Direct Variation A direct variation is formed by the variables x and y if the ratio y : x always equals a constant k, where k is a positive number.

7
**Directly Proportional**

Variables are directly proportional when y is said to vary directly with x.

8
**Constant of Proportionality**

The constant k is the constant of variation, or the constant of proportionality.

9
x hours y miles y x 1 30 2 60 3 90 4 120

10
Example 1 Does y vary directly with x in the following table? If so, find the constant of variation and write an equation for the direct variation. x y 1 3 3 9 5 15 7 21

11
x y 1 3 3 9 5 15 7 21 = 3 1 y x 3 = 21 7 y x 3 = 9 3 y x 3 = y x 3 k y = kx = 15 5 y x 3 y = 3x

12
Constant of Variation The constant of variation is the steady rate of change. The constant k is the constant of variation, or the constant of proportionality.

13
Example 2 Indicate which equations represent a direct variation. If an equation describes a direct variation, give the constant of variation. f(x) = 2.2x direct variation; k = 2.2

14
y = 4x − 1 This is not a direct variation; the variable must be a multiple of x. d = 45t This is a direct variation; k = 45. y = −2x This is not a direct variation; the coefficient of x must be positive.

15
y = mx + b y = kx

16
Example 3 Graph the direct variation y = 4x. x −1 1 y −4 4

17
y x

18
Example 4 Find k if y varies directly with x and y = 12 when x = . Write an equation for the direct variation. 1 2 y = kx k = 24 12 = k( ) 1 2 y = 24x 2(12) = k( )(2) 1 2

19
Example 5 If y varies directly with x and y = 6 when x = 2, find y when x = . 2 3 y = kx y = 3x y = 3( ) 2 3 6 = k(2) 3 = k y = 2

20
**Example Find k if y varies directly with x and y = 14 when x = 4.**

21
**Example Find k if y varies directly with x and y = 15 when x = 2.**

22
Example If y varies directly with x and y = 7 when x = 1, find y when x = 6. y = 42

23
Example If y varies directly with x and y = 27 when x = 15, find y when x = 6. 54 5 y =

24
Example Indicate which equations represent a direct variation. If an equation describes a direct variation, give the constant of variation. If not, explain.

25
y = 4x Yes. k = 4. y = 3x + 5 No. The y-intercept is not zero. y = −4x No. The slope is not positive.

Similar presentations

OK

Constant, Linear and Non-Linear Constant, Linear and Non-Linear

Constant, Linear and Non-Linear Constant, Linear and Non-Linear

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Free download ppt on diversity in living organisms class 9 Ppt on combination of resistances in parallel Ppt on biography of mahatma gandhi Ppt on 2nd world war end Ppt on digital media broadcasting Ppt on different types of dance forms Ppt on technical topics related to computer science Ppt on different types of houses for kids Ppt on management by objectives Ppt on product specifications