Linear relationships worksheet focusing on slope and rate of change with a graph and fill-in-the-blank questions.

Let's solve this step-by-step.

---

Part I: Match each blank with the correct vocabulary term

We are given a list of definitions and a list of vocabulary terms (A–F). We need to match the correct term to each blank.

Vocabulary Terms:
- A. Positive
- B. Undefined
- C. Run
- D. Zero
- E. Negative
- F. Rise

Now, let’s go through each sentence:

1. The vertical change on a graph is described as the _________.
→ Vertical change = Rise
✔ Answer: F. Rise

2. The horizontal change on a graph is described as the _________.
→ Horizontal change = Run
✔ Answer: C. Run

3. The slope of a horizontal line will always be _________.
→ A horizontal line has no vertical change → rise = 0 → slope = 0
✔ Answer: D. Zero

4. The slope of a vertical line will always be _________.
→ A vertical line has no horizontal change → run = 0 → division by zero → undefined
✔ Answer: B. Undefined

5. A graph with a _________ slope increases from left to right.
→ When a line goes up from left to right, it has a positive slope
✔ Answer: A. Positive

6. A graph with a _________ slope decreases from left to right.
→ When a line goes down from left to right, it has a negative slope
✔ Answer: E. Negative

---

✔ Part I Answers:

1. F
2. C
3. D
4. B
5. A
6. E

---

Part II: Find the slope of each line segment in the word "MATH"

We’ll use the slope formula:
> Slope = rise / run = (change in y) / (change in x)

We'll analyze each line segment using the graph.

Let’s go one by one.

#### Line 1
From point (-8, 8) to (-8, 1):
- Δx = -8 - (-8) = 0
- Δy = 1 - 8 = -7
→ Vertical line → Undefined slope
✔ Answer: Undefined

#### Line 2
From (-8, 8) to (-5, 4):
- Δx = -5 - (-8) = 3
- Δy = 4 - 8 = -4
→ Slope = -4 / 3
✔ Answer: -4/3

#### Line 3
From (-5, 4) to (-2, 8):
- Δx = -2 - (-5) = 3
- Δy = 8 - 4 = 4
→ Slope = 4 / 3
✔ Answer: 4/3

#### Line 4
From (-2, 8) to (-2, 1):
- Δx = 0
- Δy = 1 - 8 = -7
→ Vertical line → Undefined
✔ Answer: Undefined

#### Line 5
From (2, 1) to (5, 7):
- Δx = 5 - 2 = 3
- Δy = 7 - 1 = 6
→ Slope = 6 / 3 = 2
✔ Answer: 2

#### Line 6
From (5, 7) to (8, 1):
- Δx = 8 - 5 = 3
- Δy = 1 - 7 = -6
→ Slope = -6 / 3 = -2
✔ Answer: -2

#### Line 7
From (5, 4) to (8, 4):
- Δx = 8 - 5 = 3
- Δy = 4 - 4 = 0
→ Slope = 0 / 3 = 0
✔ Answer: 0

#### Line 8
From (-6, -2) to (-2, -2):
- Δx = -2 - (-6) = 4
- Δy = -2 - (-2) = 0
→ Slope = 0 / 4 = 0
✔ Answer: 0

#### Line 9
From (-2, -2) to (-2, -8):
- Δx = 0
- Δy = -8 - (-2) = -6
→ Vertical line → Undefined
✔ Answer: Undefined

#### Line 10
From (1, -2) to (1, -8):
- Δx = 0
- Δy = -8 - (-2) = -6
→ Vertical line → Undefined
✔ Answer: Undefined

#### Line 11
From (1, -5) to (7, -5):
- Δx = 7 - 1 = 6
- Δy = -5 - (-5) = 0
→ Slope = 0 / 6 = 0
✔ Answer: 0

#### Line 12
From (7, -5) to (7, -8):
- Δx = 0
- Δy = -8 - (-5) = -3
→ Vertical line → Undefined
✔ Answer: Undefined

---

✔ Part II Answers:

| Line | Slope |
|------|---------------|
| 7. Line 1 | Undefined |
| 8. Line 2 | -4/3 |
| 9. Line 3 | 4/3 |
| 10. Line 4 | Undefined |
| 11. Line 5 | 2 |
| 12. Line 6 | -2 |
| 13. Line 7 | 0 |
| 14. Line 8 | 0 |
| 15. Line 9 | Undefined |
| 16. Line 10 | Undefined |
| 17. Line 11 | 0 |
| 18. Line 12 | Undefined |

---

✔ Final Answer Summary:

#### Part I:
1. F
2. C
3. D
4. B
5. A
6. E

#### Part II:
7. Undefined
8. -4/3
9. 4/3
10. Undefined
11. 2
12. -2
13. 0
14. 0
15. Undefined
16. Undefined
17. 0
18. Undefined

---

Let me know if you'd like this formatted for printing or submission!