1. 9-10 Writing Equations
Algebra and Functions 1.5

2. Skills Needed:

3. Skills Needed:
Recognizing patterns

4. Skills Needed:
Recognizing patterns
+3
x y
4
0
2

5. Skills Needed:
Recognizing patterns
Before: You were
given the rule.
+3
x y
4
0
2

6. Skills Needed:
Recognizing patterns
Before: You were
given the rule.
+ 3
x y
4 7
0 3
2 5

7. Skills Needed:
Recognizing patterns
Before: You were
given the rule.
+ 3 ?
x y x y
4 7 2 7
0 3 3 8
2 5 4 9

8. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3 ?
x y x y
4 7 2 7
0 3 3 8
2 5 4 9

9. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3 ?
x y x y
4 7 2 7 2+5=7
0 3 3 8
2 5 4 9

10. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3 ?
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9

11. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3 ?
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9 4+5=9

12. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3 ?
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9 4+5=9

13. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9 4+5=9

14. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
THE RULE.
+ 3 + 5
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9 4+5=9

15. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
The Rule! THE RULE.
+ 3 + 5
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9 4+5=9

16. Skills Needed:
Recognizing patterns
Before: You were Today: You find a
given the rule. pattern to FIND
The Rule! THE RULE.
+ 3 + 5
x y x y
4 7 2 7 2+5=7
0 3 3 8 3+5=8
2 5 4 9 4+5=9
The equation is written y = x + 5.

18. x -3 -2 -1 0 1 2 3
y -6 -5 -4 -3 -2 1 0

19. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0

20. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
?
-3 -6
-2 -5
-1 -4
0 -3
1 -2
2 -1
3 0

21. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? Use number lines to help find
-3 -6 a pattern to identify the RULE.
-2 -5
-1 -4
0 -3
1 -2
2 -1
3 0

22. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
?
-3 -6
-2 -5
-1 -4
0 -3
1 -2
2 -1
3 0

23. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
?
-3 -6
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 -4
0 -3
1 -2
2 -1
3 0

24. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
?
-3 -6
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 -4
0 -3
1 -2
2 -1
3 0

25. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 -4
0 -3
1 -2
2 -1
3 0

26. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 -4
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 -2
2 -1
3 0

27. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 -4
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 -2
2 -1
3 0

28. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 -2
2 -1
3 0

29. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 -2
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 0

30. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 -2
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 0

31. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 0

32. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 0
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

33. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 0
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

34. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
? moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
3 0 left - 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

35. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
3 0 left - 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

36. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
- 3
moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
3 0 left - 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

37. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y -6 -5 -4 -3 -2 1 0
- 3
moves
-3 -6 left - 3
-2 -5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 -4 left - 3
0 -3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 -2 left - 3
2 -1 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
3 0 left - 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
The equation is written y = x - 3.

39. x -3 -2 -1 0 1 2 3
y 2 3 4 5 6 7 8

40. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8

41. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
?
-3 2
-2 3
-1 4
0 5
1 6
2 7
3 8

42. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? Use number lines to help find
-3 2 a pattern to identify the RULE.
-2 3
-1 4
0 5
1 6
2 7
3 8

43. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
?
-3 2
-2 3
-1 4
0 5
1 6
2 7
3 8

44. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
?
-3 2
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 4
0 5
1 6
2 7
3 8

45. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
?
-3 2
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 4
0 5
1 6
2 7
3 8

46. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 4
0 5
1 6
2 7
3 8

47. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 4
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 6
2 7
3 8

48. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
-1 4
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 6
2 7
3 8

49. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 6
2 7
3 8

50. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 6
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 8

51. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
1 6
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 8

52. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 8

53. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 8
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

54. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
3 8
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7

55. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
3 8 right
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5

56. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
? moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
+8 moves
3 8 right
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5

57. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
+8 moves
3 8 right
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5

58. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
+ 5 moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
+8 moves
3 8 right
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5

59. Rewrite x -3 -2 -1 0 1 2 3
vertically.
y 2 3 4 5 6 7 8
+ 5 moves
-3 2 right
+5
-2 3
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
-1 4 right
+5
0 5
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
moves
1 6 right
+5
2 7 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7
+8 moves
3 8 right
-7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6+7 +5
The equation is written y = x + 5.

60. Write an equation to describe the
relationship between x and y.

61. Write an equation to describe the
relationship between x and y.
x y
-2 8
-1 9
0 10
1 11
2 12

62. Write an equation to describe the
relationship between x and y.
x y x y
-2 8 -2 -4
-1 9 -1 -3
0 10 0 -2
1 11 1 -1
2 12 2 0

63. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8

64. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10

65. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10

66. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10

67. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10 y=x-2

68. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10 y=x-2

69. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10 y=x-2

70. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10 y=x-2 y=x+6

71. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10 y=x-2 y=x+6

72. Write an equation to describe the
relationship between x and y.
x y x y x y
-2 8 -2 -4 -2 4
-1 9 -1 -3 -1 5
0 10 0 -2 0 6
1 11 1 -1 1 7
2 12 2 0 2 8
y = x + 10 y=x-2 y=x+6