4.6 model direct variation day 2

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4.6 model direct variation day 2

  1. 1. EXAMPLE 2 Graph direct variation equations b. Write the equation for this line / graph
  2. 2. GUIDED PRACTICE for Examples 2 and 35. 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. SOLUTION Because y varies directly with x, the equation has the form y = ax. Use the fact that y = 6 when x = 4 to find a. y = ax Write direct variation equation. 6 = a (4) Substitute. 6 3 Solve for a. a= = 4 2
  3. 3. GUIDED PRACTICE for Examples 2 and 3 ANSWER A direct variation equation that relates x and y is y = 3 x when x = 24. y = 3 (24) = 36 2 2
  4. 4. Graph theseequations. Whatcan you say aboutthese lines?y = 2/3 xy= -3/2 x
  5. 5. • If the variables x & y vary directly, write an equation when x = 5 and y = 20.• (think y = ax)• So, would 20 = a(5)• Equation : y = 4x
  6. 6. • If the variables x & y vary directly, write an equation when x = -3 and y = 30.• What would be the value of y when x = 5?
  7. 7. EXAMPLE 4 Solve a multi-step problem SALTWATER AQUARIUMThe number s of tablespoons ofsea salt needed in a saltwater fishtank varies directly with thenumber w of gallons of water inthe tank. A pet shop ownerrecommends adding 100tablespoons of sea salt to a 20gallon 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?
  8. 8. • When x and y vary directly, there is a nonzero number a such that the following is true: y = ax a is the constant of variationFor example: y = 3x or y = -1/4xnon-example : y = 4x + 5
  9. 9. Graph theseequations. Whatcan you say aboutthese lines?y = 2/3 xy= -3/2 x
  10. 10. • If the variables x & y vary directly, write an equation when x = 5 and y = 20.• (think y = ax)• So, would 20 = a(5)• Equation : y = 4x
  11. 11. • If the variables x & y vary directly, write an equation when x = -3 and y = 30.• What would be the value of y when x = 5?
  12. 12. • Cont’ P. 257 (#23-27, 29-33, 40-42)• (45 together) Cost In Dollars Number of days
  13. 13. x 1 2 3 4 6 y 5 10 15 20 30Tell if the table represents direct variation. Ifso, write the direct variation equation.

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