1. 3.6 – Proportional & Nonproportional Relationships

2. RECALL: Direct Variation y = kx

3. RECALL: Direct Variation y = kx Proportional Relationships – direct variation (passes through origin)

4. RECALL: Direct Variation y = kx Proportional Relationships – direct variation (passes through origin) Nonproportional Relationships – any linear function that cannot be expressed by y = kx

5. Ex. 1 Write an equation in function notation for the graph.

6. Ex. 1 Write an equation in function notation for the graph.y

7. Ex. 1 Write an equation in function notation for the graph.y -1 -2

8. Ex. 1 Write an equation in function notation for the graph.y -1 -2

9. Ex. 1 Write an equation in function notation for the graph.y -1 -2 1 2

10. Ex. 1 Write an equation in function notation for the graph.y -1 -2 1 2 4

11. Ex. 1 Write an equation in function notation for the graph.y -1 -2 1 2 4

12. Ex. 1 Write an equation in function notation for the graph.
Goes through origin so
direct variation & proportional x y -1 -2 1 2 4

13. Ex. 1 Write an equation in function notation for the graph.
Goes through origin so
direct variation & proportional x y -1 -2 1 2 4 +1 +1 +1

14. Ex. 1 Write an equation in function notation for the graph.
Goes through origin so
direct variation & proportional x y -1 -2 1 2 4 +1 +2 +1 +2 +1 +2

15. Ex. 1 Write an equation in function notation for the graph.
Goes through origin so
direct variation & proportional
y = 2x x y -1 -2 1 2 4 +1 +2 +1 +2 +1 +2

16. Ex. 1 Write an equation in function notation for the graph.
Goes through origin so
direct variation & proportional
y = 2x
f(x) = 2x x y -1 -2 1 2 4 +1 +2 +1 +2 +1 +2

17. Ex. 2 Write an equation in function notation for the graph.

18. Ex. 2 Write an equation in function notation for the graph.y -1 -3 1 2 3

19. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional x y -1 -3 1 2 3

20. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional x y -1 -3 1 2 3 +1 +2 +1 +2 +1 +2

21. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional x 2x y -1 -3 1 2 3 +1 +2 +1 +2 +1 +2

22. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional x 2x y -1 -2 -3 1 2 4 3 +1 +2 +1 +2 +1 +2

23. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional
y = 2x x 2x y -1 -2 -3 1 2 4 3 +1 +2 +1 +2 +1 +2

24. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional
y = 2x x 2x y -1 -2 -3 1 2 4 3 +1 +2 +1 +2 +1 +2

25. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional
y = 2x x 2x y -1 -2 -3 1 2 4 3 -1 +1 +2 -1 +1 +2 -1 +1 +2 -1

26. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional
y = 2x – 1 x 2x y -1 -2 -3 1 2 4 3 -1 +1 +2 -1 +1 +2 -1 +1 +2 -1

27. Ex. 2 Write an equation in function notation for the graph.
DOES NOT GO through origin
so Nonproportional
y = 2x – 1
f(x) = 2x – 1 x 2x y -1 -2 -3 1 2 4 3 -1 +1 +2 -1 +1 +2 -1 +1 +2 -1

28. Ex. 3 The total snowfall each hour of a winter
Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below.
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60

29. Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below. a. Write an equation for the data.
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60

30. Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below. a. Write an equation for the data. +1 +1 +1
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60

31. Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below. a. Write an equation for the data. +1 +1 +1
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60
+1.65
+1.65
+1.65

32. Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below. a. Write an equation for the data. y = 1.65x +1 +1 +1
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60
+1.65
+1.65
+1.65

33. Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below. a. Write an equation for the data. y = 1.65x b. Describe the relationship between the hour and inches of snowfall. +1 +1 +1
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60
+1.65
+1.65
+1.65

34. Ex. 3 The total snowfall each hour of a winter snowstorm is shown in the table below. a. Write an equation for the data. y = 1.65x b. Describe the relationship between the hour and inches of snowfall. Proportional +1 +1 +1
Hour 1 2 3 4
Inches of Snowfall
1.65
3.30
4.95
6.60
+1.65
+1.65
+1.65