UST Middle School Pre-Algebra Challenge
Week 8 — Coordinate Plane & Linear Relationships
Focus: Slope intuition, tables, graphs, patterns
Weekly Format
Week 8
Part A — 15 Multiple Choice
Part B — 15 Fill in the Blank
Part C — 15 Word / Open-Response Problems
Part D — 5 Challenge Problems
Answers and step-by-step explanations are provided at the end.
Part A — Multiple Choice
Questions 1–5
1. For y=2x+1, what is y when x=1? A) 3 B) 2 C) 2 D) 5
2. For y=2x+1, what is y when x=2? A) 5 B) 3 C) 4 D) 7
3. For y=2x+1, what is y when x=3? A) 7 B) 4 C) 6 D) 9
4. For y=2x+1, what is y when x=4? A) 9 B) 5 C) 8 D) 11
5. For y=2x+1, what is y when x=5? A) 11 B) 6 C) 10 D) 13
Part A — Multiple Choice
Questions 6–10
6. For y=2x+1, what is y when x=6? A) 13 B) 7 C) 12 D) 15
7. For y=2x+1, what is y when x=7? A) 15 B) 8 C) 14 D) 17
8. For y=2x+1, what is y when x=8? A) 17 B) 9 C) 16 D) 19
9. For y=2x+1, what is y when x=9? A) 19 B) 10 C) 18 D) 21
10. For y=2x+1, what is y when x=10? A) 21 B) 11 C) 20 D) 23
Part A — Multiple Choice
Questions 11–15
11. For y=2x+1, what is y when x=11? A) 23 B) 12 C) 22 D) 25
12. For y=2x+1, what is y when x=12? A) 25 B) 13 C) 24 D) 27
13. For y=2x+1, what is y when x=13? A) 27 B) 14 C) 26 D) 29
14. For y=2x+1, what is y when x=14? A) 29 B) 15 C) 28 D) 31
15. For y=2x+1, what is y when x=15? A) 31 B) 16 C) 30 D) 33
Part B — Fill in the Blank
Questions 16–20
16. Complete the pattern y=3x−2. If x=1, y=___.
17. Complete the pattern y=3x−2. If x=2, y=___.
18. Complete the pattern y=3x−2. If x=3, y=___.
19. Complete the pattern y=3x−2. If x=4, y=___.
20. Complete the pattern y=3x−2. If x=5, y=___.
Part B — Fill in the Blank
Questions 21–25
21. Complete the pattern y=3x−2. If x=6, y=___.
22. Complete the pattern y=3x−2. If x=7, y=___.
23. Complete the pattern y=3x−2. If x=8, y=___.
24. Complete the pattern y=3x−2. If x=9, y=___.
25. Complete the pattern y=3x−2. If x=10, y=___.
Part B — Fill in the Blank
Questions 26–30
26. Complete the pattern y=3x−2. If x=11, y=___.
27. Complete the pattern y=3x−2. If x=12, y=___.
28. Complete the pattern y=3x−2. If x=13, y=___.
29. Complete the pattern y=3x−2. If x=14, y=___.
30. Complete the pattern y=3x−2. If x=15, y=___.
Part C — Word / Open Response
Questions 31–35
31. A taxi charges $10 plus $5 per mile. What is the cost for 1 miles?
32. A taxi charges $10 plus $5 per mile. What is the cost for 2 miles?
33. A taxi charges $10 plus $5 per mile. What is the cost for 3 miles?
34. A taxi charges $10 plus $5 per mile. What is the cost for 4 miles?
35. A taxi charges $10 plus $5 per mile. What is the cost for 5 miles?
Part C — Word / Open Response
Questions 36–40
36. A taxi charges $10 plus $5 per mile. What is the cost for 6 miles?
37. A taxi charges $10 plus $5 per mile. What is the cost for 7 miles?
38. A taxi charges $10 plus $5 per mile. What is the cost for 8 miles?
39. A taxi charges $10 plus $5 per mile. What is the cost for 9 miles?
40. A taxi charges $10 plus $5 per mile. What is the cost for 10 miles?
Part C — Word / Open Response
Questions 41–45
41. A taxi charges $10 plus $5 per mile. What is the cost for 11 miles?
42. A taxi charges $10 plus $5 per mile. What is the cost for 12 miles?
43. A taxi charges $10 plus $5 per mile. What is the cost for 13 miles?
44. A taxi charges $10 plus $5 per mile. What is the cost for 14 miles?
45. A taxi charges $10 plus $5 per mile. What is the cost for 15 miles?
Part D — Challenge
Questions 46–50
46. Challenge: A line follows y=−2x+7. Find y when x=3.
47. Challenge: A line follows y=−2x+7. Find y when x=4.
48. Challenge: A line follows y=−2x+7. Find y when x=5.
49. Challenge: A line follows y=−2x+7. Find y when x=6.
50. Challenge: A line follows y=−2x+7. Find y when x=7.
Answer Key — Questions 1–5
Answer + How to Solve
1. Answer: A
How to solve: Substitute x=1: y=2(1)+1=3.
2. Answer: A
How to solve: Substitute x=2: y=2(2)+1=5.
3. Answer: A
How to solve: Substitute x=3: y=2(3)+1=7.
4. Answer: A
How to solve: Substitute x=4: y=2(4)+1=9.
5. Answer: A
How to solve: Substitute x=5: y=2(5)+1=11.
Answer Key — Questions 6–10
Answer + How to Solve
6. Answer: A
How to solve: Substitute x=6: y=2(6)+1=13.
7. Answer: A
How to solve: Substitute x=7: y=2(7)+1=15.
8. Answer: A
How to solve: Substitute x=8: y=2(8)+1=17.
9. Answer: A
How to solve: Substitute x=9: y=2(9)+1=19.
10. Answer: A
How to solve: Substitute x=10: y=2(10)+1=21.
Answer Key — Questions 11–15
Answer + How to Solve
11. Answer: A
How to solve: Substitute x=11: y=2(11)+1=23.
12. Answer: A
How to solve: Substitute x=12: y=2(12)+1=25.
13. Answer: A
How to solve: Substitute x=13: y=2(13)+1=27.
14. Answer: A
How to solve: Substitute x=14: y=2(14)+1=29.
15. Answer: A
How to solve: Substitute x=15: y=2(15)+1=31.
Answer Key — Questions 16–20
Answer + How to Solve
16. Answer: 1
How to solve: Substitute x=1: 3(1)−2=1.
17. Answer: 4
How to solve: Substitute x=2: 3(2)−2=4.
18. Answer: 7
How to solve: Substitute x=3: 3(3)−2=7.
19. Answer: 10
How to solve: Substitute x=4: 3(4)−2=10.
20. Answer: 13
How to solve: Substitute x=5: 3(5)−2=13.
Answer Key — Questions 21–25
Answer + How to Solve
21. Answer: 16
How to solve: Substitute x=6: 3(6)−2=16.
22. Answer: 19
How to solve: Substitute x=7: 3(7)−2=19.
23. Answer: 22
How to solve: Substitute x=8: 3(8)−2=22.
24. Answer: 25
How to solve: Substitute x=9: 3(9)−2=25.
25. Answer: 28
How to solve: Substitute x=10: 3(10)−2=28.
Answer Key — Questions 26–30
Answer + How to Solve
26. Answer: 31
How to solve: Substitute x=11: 3(11)−2=31.
27. Answer: 34
How to solve: Substitute x=12: 3(12)−2=34.
28. Answer: 37
How to solve: Substitute x=13: 3(13)−2=37.
29. Answer: 40
How to solve: Substitute x=14: 3(14)−2=40.
30. Answer: 43
How to solve: Substitute x=15: 3(15)−2=43.
Answer Key — Questions 31–35
Answer + How to Solve
31. Answer: $15
How to solve: Linear rule: C=5m+10. Substitute m=1.
32. Answer: $20
How to solve: Linear rule: C=5m+10. Substitute m=2.
33. Answer: $25
How to solve: Linear rule: C=5m+10. Substitute m=3.
34. Answer: $30
How to solve: Linear rule: C=5m+10. Substitute m=4.
35. Answer: $35
How to solve: Linear rule: C=5m+10. Substitute m=5.
Answer Key — Questions 36–40
Answer + How to Solve
36. Answer: $40
How to solve: Linear rule: C=5m+10. Substitute m=6.
37. Answer: $45
How to solve: Linear rule: C=5m+10. Substitute m=7.
38. Answer: $50
How to solve: Linear rule: C=5m+10. Substitute m=8.
39. Answer: $55
How to solve: Linear rule: C=5m+10. Substitute m=9.
40. Answer: $60
How to solve: Linear rule: C=5m+10. Substitute m=10.
Answer Key — Questions 41–45
Answer + How to Solve
41. Answer: $65
How to solve: Linear rule: C=5m+10. Substitute m=11.
42. Answer: $70
How to solve: Linear rule: C=5m+10. Substitute m=12.
43. Answer: $75
How to solve: Linear rule: C=5m+10. Substitute m=13.
44. Answer: $80
How to solve: Linear rule: C=5m+10. Substitute m=14.
45. Answer: $85
How to solve: Linear rule: C=5m+10. Substitute m=15.
Answer Key — Questions 46–50
Answer + How to Solve
46. Answer: 1
How to solve: Substitute x=3: y=−2(3)+7=1.
47. Answer: -1
How to solve: Substitute x=4: y=−2(4)+7=-1.
48. Answer: -3
How to solve: Substitute x=5: y=−2(5)+7=-3.
49. Answer: -5
How to solve: Substitute x=6: y=−2(6)+7=-5.
50. Answer: -7
How to solve: Substitute x=7: y=−2(7)+7=-7.