Math worksheet for completing function tables based on linear equations.

To solve the problem, we need to complete the function tables for each given equation by substituting the provided \( x \)-values into the equations and calculating the corresponding \( y \)-values. Let's go through each equation step by step.

---

Equation 1: \( y = -\frac{1}{5}x - 6 \)

| \( x \) | \( y \) |
|---------|---------|
| 9 | |
| -1 | |
| 5 | |
| -7 | |
| 3 | |

#### Substituting values:
1. For \( x = 9 \):
\[
y = -\frac{1}{5}(9) - 6 = -\frac{9}{5} - 6 = -1.8 - 6 = -7.8
\]

2. For \( x = -1 \):
\[
y = -\frac{1}{5}(-1) - 6 = \frac{1}{5} - 6 = 0.2 - 6 = -5.8
\]

3. For \( x = 5 \):
\[
y = -\frac{1}{5}(5) - 6 = -1 - 6 = -7
\]

4. For \( x = -7 \):
\[
y = -\frac{1}{5}(-7) - 6 = \frac{7}{5} - 6 = 1.4 - 6 = -4.6
\]

5. For \( x = 3 \):
\[
y = -\frac{1}{5}(3) - 6 = -\frac{3}{5} - 6 = -0.6 - 6 = -6.6
\]

Completed Table:
| \( x \) | \( y \) |
|---------|---------|
| 9 | -7.8 |
| -1 | -5.8 |
| 5 | -7 |
| -7 | -4.6 |
| 3 | -6.6 |

---

Equation 2: \( y = 5x \)

| \( x \) | \( y \) |
|---------|---------|
| -5 | |
| -4 | |
| -1 | |

#### Substituting values:
1. For \( x = -5 \):
\[
y = 5(-5) = -25
\]

2. For \( x = -4 \):
\[
y = 5(-4) = -20
\]

3. For \( x = -1 \):
\[
y = 5(-1) = -5
\]

Completed Table:
| \( x \) | \( y \) |
|---------|---------|
| -5 | -25 |
| -4 | -20 |
| -1 | -5 |

---

Equation 5: \( y = -\frac{1}{8}x + 6 \)

| \( x \) | \( y \) |
|---------|---------|
| 5 | |
| -2 | |
| 7 | |
| 6 | |
| -9 | |

#### Substituting values:
1. For \( x = 5 \):
\[
y = -\frac{1}{8}(5) + 6 = -\frac{5}{8} + 6 = -0.625 + 6 = 5.375
\]

2. For \( x = -2 \):
\[
y = -\frac{1}{8}(-2) + 6 = \frac{2}{8} + 6 = 0.25 + 6 = 6.25
\]

3. For \( x = 7 \):
\[
y = -\frac{1}{8}(7) + 6 = -\frac{7}{8} + 6 = -0.875 + 6 = 5.125
\]

4. For \( x = 6 \):
\[
y = -\frac{1}{8}(6) + 6 = -\frac{6}{8} + 6 = -0.75 + 6 = 5.25
\]

5. For \( x = -9 \):
\[
y = -\frac{1}{8}(-9) + 6 = \frac{9}{8} + 6 = 1.125 + 6 = 7.125
\]

Completed Table:
| \( x \) | \( y \) |
|---------|---------|
| 5 | 5.375 |
| -2 | 6.25 |
| 7 | 5.125 |
| 6 | 5.25 |
| -9 | 7.125 |

---

Equation 6: \( y = x - 6 \)

| \( x \) | \( y \) |
|---------|---------|
| 7 | |
| 2 | |
| 0 | |

#### Substituting values:
1. For \( x = 7 \):
\[
y = 7 - 6 = 1
\]

2. For \( x = 2 \):
\[
y = 2 - 6 = -4
\]

3. For \( x = 0 \):
\[
y = 0 - 6 = -6
\]

Completed Table:
| \( x \) | \( y \) |
|---------|---------|
| 7 | 1 |
| 2 | -4 |
| 0 | -6 |

---

Equation 9: \( y = 7x - 5 \)

| \( x \) | \( y \) |
|---------|---------|
| 9 | |
| 7 | |
| 3 | |
| -9 | |
| 2 | |

#### Substituting values:
1. For \( x = 9 \):
\[
y = 7(9) - 5 = 63 - 5 = 58
\]

2. For \( x = 7 \):
\[
y = 7(7) - 5 = 49 - 5 = 44
\]

3. For \( x = 3 \):
\[
y = 7(3) - 5 = 21 - 5 = 16
\]

4. For \( x = -9 \):
\[
y = 7(-9) - 5 = -63 - 5 = -68
\]

5. For \( x = 2 \):
\[
y = 7(2) - 5 = 14 - 5 = 9
\]

Completed Table:
| \( x \) | \( y \) |
|---------|---------|
| 9 | 58 |
| 7 | 44 |
| 3 | 16 |
| -9 | -68 |
| 2 | 9 |

---

Equation 10: \( y = -4x \)

| \( x \) | \( y \) |
|---------|---------|
| 7 | |
| 6 | |
| 2 | |

#### Substituting values:
1. For \( x = 7 \):
\[
y = -4(7) = -28
\]

2. For \( x = 6 \):
\[
y = -4(6) = -24
\]

3. For \( x = 2 \):
\[
y = -4(2) = -8
\]

Completed Table:
| \( x \) | \( y \) |
|---------|---------|
| 7 | -28 |
| 6 | -24 |
| 2 | -8 |

---

Final Answer:

\[
\boxed{
\begin{array}{c|c}
\text{Equation 1} & \begin{array}{c|c}
x & y \\
\hline
9 & -7.8 \\
-1 & -5.8 \\
5 & -7 \\
-7 & -4.6 \\
3 & -6.6 \\
\end{array} \\
\text{Equation 2} & \begin{array}{c|c}
x & y \\
\hline
-5 & -25 \\
-4 & -20 \\
-1 & -5 \\
\end{array} \\
\text{Equation 5} & \begin{array}{c|c}
x & y \\
\hline
5 & 5.375 \\
-2 & 6.25 \\
7 & 5.125 \\
6 & 5.25 \\
-9 & 7.125 \\
\end{array} \\
\text{Equation 6} & \begin{array}{c|c}
x & y \\
\hline
7 & 1 \\
2 & -4 \\
0 & -6 \\
\end{array} \\
\text{Equation 9} & \begin{array}{c|c}
x & y \\
\hline
9 & 58 \\
7 & 44 \\
3 & 16 \\
-9 & -68 \\
2 & 9 \\
\end{array} \\
\text{Equation 10} & \begin{array}{c|c}
x & y \\
\hline
7 & -28 \\
6 & -24 \\
2 & -8 \\
\end{array}
\end{array}
}
\]