Slope and Rate of Change online exercise for - Free Printable

Let's solve this step-by-step.

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Part I: Match each blank with the correct vocabulary term

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

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), so slope = 0/any number = 0
✔ Answer: D. Zero

4. The slope of a vertical line will always be _________.
→ A vertical line has no horizontal change (run = 0), so slope = any number / 0 → 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

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

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Part II: Find the slope of each line segment

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

We'll calculate for each line segment using the coordinates from the graph.

Let’s analyze each line:

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#### Line 1: From (-8, 8) to (-8, 1)
- Change in x (run): -8 - (-8) = 0
- Change in y (rise): 1 - 8 = -7
- Slope = -7 / 0 → Undefined
✔ Answer: Undefined

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#### Line 2: From (-8, 8) to (-5, 4)
- Run: -5 - (-8) = 3
- Rise: 4 - 8 = -4
- Slope = -4 / 3 = -4/3
✔ Answer: -4/3

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#### Line 3: From (-5, 4) to (-2, 8)
- Run: -2 - (-5) = 3
- Rise: 8 - 4 = 4
- Slope = 4 / 3 = 4/3
✔ Answer: 4/3

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#### Line 4: From (-2, 8) to (-2, 1)
- Run: -2 - (-2) = 0
- Rise: 1 - 8 = -7
- Slope = -7 / 0 → Undefined
✔ Answer: Undefined

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

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

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

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#### Line 8: From (-7, -2) to (-2, -2)
- Run: -2 - (-7) = 5
- Rise: -2 - (-2) = 0
- Slope = 0 / 5 = 0
✔ Answer: 0

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#### Line 9: From (-2, -2) to (-2, -8)
- Run: -2 - (-2) = 0
- Rise: -8 - (-2) = -6
- Slope = -6 / 0 → Undefined
✔ Answer: Undefined

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#### Line 10: From (1, -2) to (1, -8)
- Run: 1 - 1 = 0
- Rise: -8 - (-2) = -6
- Slope = -6 / 0 → Undefined
✔ Answer: Undefined

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

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#### Line 12: From (7, -5) to (7, -8)
- Run: 7 - 7 = 0
- Rise: -8 - (-5) = -3
- Slope = -3 / 0 → Undefined
✔ Answer: Undefined

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✔ Final Answers for Part II:

| Line | Slope |
|------|-------------|
| 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 |

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✔ Complete Answer Key:

#### 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

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📌 Explanation Summary:

- Slope = rise/run
- Vertical lines have undefined slope (division by zero).
- Horizontal lines have zero slope.
- Positive slope: line rises from left to right.
- Negative slope: line falls from left to right.

This worksheet reinforces understanding of slope as a rate of change and how it applies to real-world graphs and geometric shapes like letters.

Let me know if you'd like this formatted as a printable answer sheet!