5 – 4 A: Direct Variation

1. 5 – 4 A: Direct Variation

2. Homework Review A line has a slope of 5 and passes through the points (4,3) and (2,y). What is the value of y? y = -7

3. Homework Review A line passes through the origin and has a slope of . Through which quadrants does the line pass? II and IV

4. Definitions Direct variation – linear relationship between two variables that can be written in the form y = kx Constant of variation – the fixed number (k) in a direct variation (the coefficient) **This is another expression that means slope or rate of change.***

5. Direct Variation • Will be a straight line when graphed • ALWAYS passes through the origin (0,0)

6. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 2x Yes k = 2

7. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 1/3 x Yes k = 1/3

8. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = - ½x Yes k = -½

9. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 2x + 3 No

10. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = ½x - 6 No

11. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. 2y = x

12. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. 2y = x 2 2 y = ½ x Yes, this is a direct variation. ½ is the constant of variation.

13. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y + 1 = 2x .

14. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y + 1 = 2x Solve for y. - 1 - 1 . y = 2x – 1 . This is not in the form y = kx, so this is not a direct variation.

15. Work with your partner. Page 214 (1-4)

16. Notes: The graph of a direct variation is a line that passes through the origin (0 0). The constant of variation (k) is the slope of the line.

17. Does this graph represent a direct variation? • Yes, the line passes through the origin, so this is a direct variation. • What is the slope of the line (constant of variation)? k = 1

18. Does this graph represent a direct variation? • Yes, the line passes through the origin, so this is a direct variation. • What is the constant of variation? k = -½

19. Does this graph represent a direct variation? • No, the line does not pass through the origin, so this is NOT a direct variation.

20. Does this graph represent a direct variation? • No, the line does not pass through the origin, so this is NOT a direct variation.

21. Does this graph represent a direct variation? • Yes, the line passes through the origin, so this is a direct variation. • What is the constant of variation? k = 2 y = 2x 22 20 18 16 14 12 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10

22. Does this graph represent a direct variation? • No, this is not a straight line, so this is NOT a direct variation.

23. Let’ look at: Page 214 (7-8)

24. Partner Talk Page 215 (19-24) Homework: Page 214 (10-13, 16-17)