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UST Middle School Algebra I Challenge

Week 6 — Writing & Graphing Linear Equations

Focus: Slope-intercept form, point-slope ideas, intercepts

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Weekly Format

Week 6

Part A — 15 Multiple Choice

Part B — 15 Fill in the Blank

Part C — 15 Word / Open-Response Problems

Part D — 5 Challenge Problems

Answer key and step-by-step explanations follow the questions.

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Part A — Multiple Choice

Questions 1–5

1. Which equation has slope 3 and y-intercept 3? A) y=3x+3 B) y=3x+3 C) y=3x−3 D) x=3y+3

2. Which equation has slope 3 and y-intercept 4? A) y=3x+4 B) y=4x+3 C) y=3x−4 D) x=3y+4

3. Which equation has slope 3 and y-intercept 5? A) y=3x+5 B) y=5x+3 C) y=3x−5 D) x=3y+5

4. Which equation has slope 3 and y-intercept 6? A) y=3x+6 B) y=6x+3 C) y=3x−6 D) x=3y+6

5. Which equation has slope 3 and y-intercept 7? A) y=3x+7 B) y=7x+3 C) y=3x−7 D) x=3y+7

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Part A — Multiple Choice

Questions 6–10

6. Which equation has slope 3 and y-intercept 8? A) y=3x+8 B) y=8x+3 C) y=3x−8 D) x=3y+8

7. Which equation has slope 3 and y-intercept 9? A) y=3x+9 B) y=9x+3 C) y=3x−9 D) x=3y+9

8. Which equation has slope 3 and y-intercept 10? A) y=3x+10 B) y=10x+3 C) y=3x−10 D) x=3y+10

9. Which equation has slope 3 and y-intercept 11? A) y=3x+11 B) y=11x+3 C) y=3x−11 D) x=3y+11

10. Which equation has slope 3 and y-intercept 12? A) y=3x+12 B) y=12x+3 C) y=3x−12 D) x=3y+12

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Part A — Multiple Choice

Questions 11–15

11. Which equation has slope 3 and y-intercept 13? A) y=3x+13 B) y=13x+3 C) y=3x−13 D) x=3y+13

12. Which equation has slope 3 and y-intercept 14? A) y=3x+14 B) y=14x+3 C) y=3x−14 D) x=3y+14

13. Which equation has slope 3 and y-intercept 15? A) y=3x+15 B) y=15x+3 C) y=3x−15 D) x=3y+15

14. Which equation has slope 3 and y-intercept 16? A) y=3x+16 B) y=16x+3 C) y=3x−16 D) x=3y+16

15. Which equation has slope 3 and y-intercept 17? A) y=3x+17 B) y=17x+3 C) y=3x−17 D) x=3y+17

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Part B — Fill in the Blank

Questions 16–20

16. For y=−2x+2, the y-intercept is ___.

17. For y=−2x+3, the y-intercept is ___.

18. For y=−2x+4, the y-intercept is ___.

19. For y=−2x+5, the y-intercept is ___.

20. For y=−2x+6, the y-intercept is ___.

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Part B — Fill in the Blank

Questions 21–25

21. For y=−2x+7, the y-intercept is ___.

22. For y=−2x+8, the y-intercept is ___.

23. For y=−2x+9, the y-intercept is ___.

24. For y=−2x+10, the y-intercept is ___.

25. For y=−2x+11, the y-intercept is ___.

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Part B — Fill in the Blank

Questions 26–30

26. For y=−2x+12, the y-intercept is ___.

27. For y=−2x+13, the y-intercept is ___.

28. For y=−2x+14, the y-intercept is ___.

29. For y=−2x+15, the y-intercept is ___.

30. For y=−2x+16, the y-intercept is ___.

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Part C — Word / Open Response

Questions 31–35

31. A service charges $12 initially plus $4 per hour. Write the linear equation for total C after h hours.

32. A service charges $13 initially plus $4 per hour. Write the linear equation for total C after h hours.

33. A service charges $14 initially plus $4 per hour. Write the linear equation for total C after h hours.

34. A service charges $15 initially plus $4 per hour. Write the linear equation for total C after h hours.

35. A service charges $16 initially plus $4 per hour. Write the linear equation for total C after h hours.

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Part C — Word / Open Response

Questions 36–40

36. A service charges $17 initially plus $4 per hour. Write the linear equation for total C after h hours.

37. A service charges $18 initially plus $4 per hour. Write the linear equation for total C after h hours.

38. A service charges $19 initially plus $4 per hour. Write the linear equation for total C after h hours.

39. A service charges $20 initially plus $4 per hour. Write the linear equation for total C after h hours.

40. A service charges $21 initially plus $4 per hour. Write the linear equation for total C after h hours.

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Part C — Word / Open Response

Questions 41–45

41. A service charges $22 initially plus $4 per hour. Write the linear equation for total C after h hours.

42. A service charges $23 initially plus $4 per hour. Write the linear equation for total C after h hours.

43. A service charges $24 initially plus $4 per hour. Write the linear equation for total C after h hours.

44. A service charges $25 initially plus $4 per hour. Write the linear equation for total C after h hours.

45. A service charges $26 initially plus $4 per hour. Write the linear equation for total C after h hours.

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Part D — Challenge

Questions 46–50

46. Challenge: Write the equation of a line with slope −2 through (0,2).

47. Challenge: Write the equation of a line with slope −2 through (0,3).

48. Challenge: Write the equation of a line with slope −2 through (0,4).

49. Challenge: Write the equation of a line with slope −2 through (0,5).

50. Challenge: Write the equation of a line with slope −2 through (0,6).

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Answer Key — Questions 1–5

Answer + How to Solve

1. Answer: A

How to solve: Slope-intercept form is y=mx+b.

2. Answer: A

How to solve: Slope-intercept form is y=mx+b.

3. Answer: A

How to solve: Slope-intercept form is y=mx+b.

4. Answer: A

How to solve: Slope-intercept form is y=mx+b.

5. Answer: A

How to solve: Slope-intercept form is y=mx+b.

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Answer Key — Questions 6–10

Answer + How to Solve

6. Answer: A

How to solve: Slope-intercept form is y=mx+b.

7. Answer: A

How to solve: Slope-intercept form is y=mx+b.

8. Answer: A

How to solve: Slope-intercept form is y=mx+b.

9. Answer: A

How to solve: Slope-intercept form is y=mx+b.

10. Answer: A

How to solve: Slope-intercept form is y=mx+b.

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Answer Key — Questions 11–15

Answer + How to Solve

11. Answer: A

How to solve: Slope-intercept form is y=mx+b.

12. Answer: A

How to solve: Slope-intercept form is y=mx+b.

13. Answer: A

How to solve: Slope-intercept form is y=mx+b.

14. Answer: A

How to solve: Slope-intercept form is y=mx+b.

15. Answer: A

How to solve: Slope-intercept form is y=mx+b.

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Answer Key — Questions 16–20

Answer + How to Solve

16. Answer: 2

How to solve: In y=mx+b, b is the y-intercept.

17. Answer: 3

How to solve: In y=mx+b, b is the y-intercept.

18. Answer: 4

How to solve: In y=mx+b, b is the y-intercept.

19. Answer: 5

How to solve: In y=mx+b, b is the y-intercept.

20. Answer: 6

How to solve: In y=mx+b, b is the y-intercept.

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Answer Key — Questions 21–25

Answer + How to Solve

21. Answer: 7

How to solve: In y=mx+b, b is the y-intercept.

22. Answer: 8

How to solve: In y=mx+b, b is the y-intercept.

23. Answer: 9

How to solve: In y=mx+b, b is the y-intercept.

24. Answer: 10

How to solve: In y=mx+b, b is the y-intercept.

25. Answer: 11

How to solve: In y=mx+b, b is the y-intercept.

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Answer Key — Questions 26–30

Answer + How to Solve

26. Answer: 12

How to solve: In y=mx+b, b is the y-intercept.

27. Answer: 13

How to solve: In y=mx+b, b is the y-intercept.

28. Answer: 14

How to solve: In y=mx+b, b is the y-intercept.

29. Answer: 15

How to solve: In y=mx+b, b is the y-intercept.

30. Answer: 16

How to solve: In y=mx+b, b is the y-intercept.

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Answer Key — Questions 31–35

Answer + How to Solve

31. Answer: C=4h+12