Math worksheet for calculating slope between two points using given x and f(x) values.

To solve the problem of finding the average slope between two points, we use the formula for the slope of a line:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

We will calculate the slope for each pair of points given in the problem. Let's go through each part step by step.

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1) Slope between \( f(5) \) and \( f(12) \)

From the table:
- \( f(5) = -0.4 \)
- \( f(12) = -6 \)

Using the slope formula:
\[
\text{slope} = \frac{f(12) - f(5)}{12 - 5} = \frac{-6 - (-0.4)}{12 - 5} = \frac{-6 + 0.4}{7} = \frac{-5.6}{7} = -0.8
\]

So, the slope is:
\[
\boxed{-0.80}
\]

---

2) Slope between \( f(-1) \) and \( f(13) \)

From the table:
- \( f(-1) = -1 \)
- \( f(13) = 1 \)

Using the slope formula:
\[
\text{slope} = \frac{f(13) - f(-1)}{13 - (-1)} = \frac{1 - (-1)}{13 + 1} = \frac{1 + 1}{14} = \frac{2}{14} = \frac{1}{7} \approx 0.14
\]

So, the slope is:
\[
\boxed{0.14}
\]

---

3) Slope between \( f(2) \) and \( f(1) \)

From the table:
- \( f(2) = 0.25 \)
- \( f(1) = 0.01 \)

Using the slope formula:
\[
\text{slope} = \frac{f(2) - f(1)}{2 - 1} = \frac{0.25 - 0.01}{2 - 1} = \frac{0.24}{1} = 0.24
\]

So, the slope is:
\[
\boxed{0.24}
\]

---

4) Slope between \( f(-7) \) and \( f(7) \)

From the table:
- \( f(-7) = 7 \)
- \( f(7) = -9 \)

Using the slope formula:
\[
\text{slope} = \frac{f(7) - f(-7)}{7 - (-7)} = \frac{-9 - 7}{7 + 7} = \frac{-16}{14} = -\frac{8}{7} \approx -1.14
\]

So, the slope is:
\[
\boxed{-1.14}
\]

---

5) Slope between \( f(-11) \) and \( f(6) \)

From the table:
- \( f(-11) = 2 \)
- \( f(6) = 2.99 \)

Using the slope formula:
\[
\text{slope} = \frac{f(6) - f(-11)}{6 - (-11)} = \frac{2.99 - 2}{6 + 11} = \frac{0.99}{17} \approx 0.06
\]

So, the slope is:
\[
\boxed{0.06}
\]

---

6) Slope between \( f(7) \) and \( f(0) \)

From the table:
- \( f(7) = -4.4 \)
- \( f(0) = -0.7 \)

Using the slope formula:
\[
\text{slope} = \frac{f(7) - f(0)}{7 - 0} = \frac{-4.4 - (-0.7)}{7} = \frac{-4.4 + 0.7}{7} = \frac{-3.7}{7} \approx -0.53
\]

So, the slope is:
\[
\boxed{-0.53}
\]

---

Final Answers:

1. \(\boxed{-0.80}\)
2. \(\boxed{0.14}\)
3. \(\boxed{0.24}\)
4. \(\boxed{-1.14}\)
5. \(\boxed{0.06}\)
6. \(\boxed{-0.53}\)

These are the slopes rounded to the nearest hundredth.