4.6 model direct variation day 2
- 1. EXAMPLE 2 Graph direct variation equations b. Write the equation for this line / graph
- 2. GUIDED PRACTICE for Examples 2 and 3 5. 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. 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. Graph these equations. What can you say about these lines? y = 2/3 x y= -3/2 x
- 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. • 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. EXAMPLE 4 Solve a multi-step problem SALTWATER AQUARIUM The number s of tablespoons of sea salt needed in a saltwater fish tank varies directly with the number w of gallons of water 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?
- 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 variation For example: y = 3x or y = -1/4x non-example : y = 4x + 5
- 9. Graph these equations. What can you say about these lines? y = 2/3 x y= -3/2 x
- 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. • 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. • Cont’ P. 257 (#23-27, 29-33, 40-42) • (45 together) Cost In Dollars Number of days
- 13. x 1 2 3 4 6 y 5 10 15 20 30 Tell if the table represents direct variation. If so, write the direct variation equation.