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Algebra I

Algebra I. 4.6 Model Direct Variation. Vocabulary. Constant of Variation: the number by which x and y are related Direct Variation: When y = kx and k does not equal zero. 2 x – 3 y = 0. – x + y = 4. a. b. EXAMPLE 1.

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Algebra I

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  1. Algebra I 4.6 Model Direct Variation

  2. Vocabulary • Constant of Variation: the number by which x and y are related • Direct Variation: When y = kx and k does not equal zero

  3. 2x – 3y = 0 – x + y = 4 a. b. EXAMPLE 1 Tell whether the equation represents direct variation. If so, identify the constant of variation. Yes; y = 2/3x so k = 2/3 NO

  4. GUIDED PRACTICE Tell whether the equation represents direct variation. If so, identify the constant of variation. 1. – x + y = 1 No; it does not vary directly. Yes; it does vary directly. y = -2x Constant = -2 2. 2x +y = 0 Yes; it does vary directly. y = 4/5x Constant = 4/5 3. 4x – 5y = 0

  5. 2 3 a. b. y = – 3x y= x y y 10 10 x x -10 -10 -10 -10 10 10 EXAMPLE 2 Graph the direct variation equation.

  6. a. Write the direct variation equation. Find the value of ywhen x=30. b. EXAMPLE 3 The graph of a direct variation equation is shown. y=ax 2=a (– 1) Plug in 30 for x –2 =a y = -2x y = -2 (30) y = -60 So, the equation is y = -2x

  7. y 10 x -10 -10 10 GUIDED PRACTICE 4. Graph the direct variation equation. y = 2x Properties of Graphs of Direct Variation Equations • The graph of a direct variation equation is a line through the origin. • The slope of the graph of y = ax is a.

  8. 6 3 4 2 a = = GUIDED PRACTICE • The graph of a direct variation on equation passes • through the point (4,6). Write the direct variation equation and find the value of y when x =24. y=ax y = 3/2x 6=a (4) y = 3/2 (24) y = 36 So, y = 3/2x

  9. EXAMPLE 4 SALTWATER AQUARIUM The number of tablespoons, s, of sea salt needed in a saltwater fish tank varies directly with the numberof gallons of water, w, in the tank. A pet shop owner recommends adding 100 tablespoons of sea salt to a 20 gallon tank. • Write a direct variation equation that relates w and s. • How many tablespoons of salt should be added to a 30 gallon saltwater fish tank?

  10. EXAMPLE 4 s= aw a. b. s = 5w 100=a(20) s = 5 (30) 5 =a s = 150 Therefore, 150 tablespoons of salt are needed. So, s = 5w

  11. ONLINE MUSIC The table shows the cost Cof downloading ssongs at an Internet music site. a. Explain why Cvaries directly with s. b. Write a direct variation equation that relates sand C. EXAMPLE 5

  12. To explain why Cvaries directly with s, compare the ratios for all data pairs (s, C ): 2.97 4.95 6.93 a. 0.99. = = = 5 7 3 C s b. A direct variation equation is C=0.99s. EXAMPLE 5 SOLUTION Because the ratios all equal 0.99,Cvaries directly with s.

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