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Solve. Exercise 5 = 3x x = 5353 5353. 4 = k 1313 1313 Solve. k = 12 Exercise.

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Presentation on theme: "Solve. Exercise 5 = 3x x = 5353 5353. 4 = k 1313 1313 Solve. k = 12 Exercise."— Presentation transcript:

1 Solve. Exercise 5 = 3x x =

2 4 = k Solve. k = 12 Exercise

3 = = y 25 Solve. y = Exercise

4 = = 25 x Solve x = Exercise

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

6 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. Direct Variation

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

8 The constant k is the constant of variation, or the constant of proportionality. Constant of Proportionality

9 x hoursy miles yxyx

10 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 Example 1

11 x y y = 3x = = yxyx yxyx = = 3 3 = = yxyx yxyx = = 3 3 = = 15 5 yxyx yxyx = = 3 3 = = 21 7 yxyx yxyx = = 3 3 = = yxyx yxyx = = 3 3 k k y = kx

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

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

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

15 y = kx y = mx + b

16 Graph the direct variation y = 4x. y −4 0 4 x −1 0 1 Example 3

17 x x y y

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

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

20 Find k if y varies directly with x and y = 14 when x = 4. k = 3.5 Example

21 Find k if y varies directly with x and y = 15 when x = 2. k = 7.5 Example

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

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

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

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


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