Sol A 6 Finding Slope And Rate Of Change - Fill Online, Printable ... - Free Printable

Since I can't view or access images directly, I’ll help you solve the problems based on the text you've provided. Let's go through each part of the worksheet step by step.

---

Worksheet: Finding Slope and Rate of Change

#### Part 1: Plot the points and draw a line through them. Then tell whether the slope of the line is positive, negative, zero, or undefined.

We use the formula for slope:
$$
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
$$

Let’s evaluate each:

1. (1, 4) and (3, 4)
$$
\text{slope} = \frac{4 - 4}{3 - 1} = \frac{0}{2} = 0
$$
→ Zero slope (horizontal line)

2. (-3, 0) and (-1, 3)
$$
\text{slope} = \frac{3 - 0}{-1 - (-3)} = \frac{3}{2} = 1.5
$$
→ Positive slope

3. (7, 1) and (-2, 1)
$$
\text{slope} = \frac{1 - 1}{-2 - 7} = \frac{0}{-9} = 0
$$
→ Zero slope

4. (-8, -3) and (-3, -2)
$$
\text{slope} = \frac{-2 - (-3)}{-3 - (-8)} = \frac{1}{5} = 0.2
$$
→ Positive slope

---

#### Part 2: Find the slope of the line that passes through the points.

5. (2, -3) and (7, 7)
$$
\text{slope} = \frac{7 - (-3)}{7 - 2} = \frac{10}{5} = 2
$$

6. (0, 0) and (5, 10)
$$
\text{slope} = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2
$$

7. (3, -2) and (3, 8)
$$
\text{slope} = \frac{8 - (-2)}{3 - 3} = \frac{10}{0} = \text{undefined}
$$
→ Undefined slope (vertical line)

8. (1, 0) and (8, 0)
$$
\text{slope} = \frac{0 - 0}{8 - 1} = \frac{0}{7} = 0
$$

9. (-8, -8) and (-2, -2)
$$
\text{slope} = \frac{-2 - (-8)}{-2 - (-8)} = \frac{6}{6} = 1
$$

10. (-5, -6) and (1, -2)
$$
\text{slope} = \frac{-2 - (-6)}{1 - (-5)} = \frac{4}{6} = \frac{2}{3}
$$

---

#### Part 3: Find the slope of the line that passes through the points. (Graphs are given)

Since we can’t see the graphs, I'll explain how to find slope from a graph:

- Pick two points on the line.
- Use rise over run:
$$
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}
$$

But let's assume typical values based on common graph patterns:

11. Graph 1: Line goes up from left to right — positive slope.
Suppose it goes from (0, 0) to (2, 4):
$$
\text{slope} = \frac{4 - 0}{2 - 0} = 2
$$
→ Slope = 2

12. Graph 2: Line goes up slowly — positive but small.
From (0, 1) to (4, 3):
$$
\text{slope} = \frac{3 - 1}{4 - 0} = \frac{2}{4} = 0.5
$$
→ Slope = 0.5

13. Graph 3: Line goes down from left to right — negative slope.
From (0, 4) to (4, 0):
$$
\text{slope} = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1
$$
→ Slope = -1

14. Graph 4: Horizontal line — no change in y → slope = 0
→ Slope = 0

---

#### Problem 15: A ramp has a rise of 10 feet and a run of 50 feet. Find its slope.

Use:
$$
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{10}{50} = \frac{1}{5} = 0.2
$$

→ Slope = 0.2

---

✔ Final Answers:

1. Zero
2. Positive
3. Zero
4. Positive
5. 2
6. 2
7. Undefined
8. 0
9. 1
10. $ \frac{2}{3} $
11. 2 (example)
12. 0.5 (example)
13. -1 (example)
14. 0
15. 0.2

> ⚠️ Note: For questions 11–14, actual answers depend on the exact graphs. If you can describe the graphs (e.g., "line goes from (0,0) to (4,2)") or provide coordinates, I can give precise slopes.

Let me know if you'd like help with any specific problem!