Math worksheet for practicing straight line equations and filling in tables of values.

Problem Overview:

The task involves completing tables of values for given linear equations in the form \( y = mx + c \). Each table corresponds to a specific equation, and we need to calculate the \( y \)-values for the given \( x \)-values.

General Approach:

For each equation \( y = mx + c \):
1. Substitute the given \( x \)-values into the equation.
2. Calculate the corresponding \( y \)-values using the formula \( y = mx + c \).
3. Fill in the table with the calculated \( y \)-values.

Solution:

#### Equation 1: \( y = 4x - 2 \)

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | | | | | | | | |

- For \( x = -3 \): \( y = 4(-3) - 2 = -12 - 2 = -14 \)
- For \( x = -2 \): \( y = 4(-2) - 2 = -8 - 2 = -10 \)
- For \( x = -1 \): \( y = 4(-1) - 2 = -4 - 2 = -6 \)
- For \( x = 0 \): \( y = 4(0) - 2 = 0 - 2 = -2 \)
- For \( x = 1 \): \( y = 4(1) - 2 = 4 - 2 = 2 \)
- For \( x = 2 \): \( y = 4(2) - 2 = 8 - 2 = 6 \)
- For \( x = 3 \): \( y = 4(3) - 2 = 12 - 2 = 10 \)
- For \( x = 4 \): \( y = 4(4) - 2 = 16 - 2 = 14 \)

Completed Table:

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | -14| -10| -6 | -2| 2 | 6 | 10| 14|

---

#### Equation 2: \( y = 3x + 2 \)

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | | | | | | | | |

- For \( x = -3 \): \( y = 3(-3) + 2 = -9 + 2 = -7 \)
- For \( x = -2 \): \( y = 3(-2) + 2 = -6 + 2 = -4 \)
- For \( x = -1 \): \( y = 3(-1) + 2 = -3 + 2 = -1 \)
- For \( x = 0 \): \( y = 3(0) + 2 = 0 + 2 = 2 \)
- For \( x = 1 \): \( y = 3(1) + 2 = 3 + 2 = 5 \)
- For \( x = 2 \): \( y = 3(2) + 2 = 6 + 2 = 8 \)
- For \( x = 3 \): \( y = 3(3) + 2 = 9 + 2 = 11 \)
- For \( x = 4 \): \( y = 3(4) + 2 = 12 + 2 = 14 \)

Completed Table:

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | -7 | -4 | -1 | 2 | 5 | 8 | 11| 14|

---

#### Equation 3: \( y = 0.5x + 1 \)

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | | | | | | | | |

- For \( x = -3 \): \( y = 0.5(-3) + 1 = -1.5 + 1 = -0.5 \)
- For \( x = -2 \): \( y = 0.5(-2) + 1 = -1 + 1 = 0 \)
- For \( x = -1 \): \( y = 0.5(-1) + 1 = -0.5 + 1 = 0.5 \)
- For \( x = 0 \): \( y = 0.5(0) + 1 = 0 + 1 = 1 \)
- For \( x = 1 \): \( y = 0.5(1) + 1 = 0.5 + 1 = 1.5 \)
- For \( x = 2 \): \( y = 0.5(2) + 1 = 1 + 1 = 2 \)
- For \( x = 3 \): \( y = 0.5(3) + 1 = 1.5 + 1 = 2.5 \)
- For \( x = 4 \): \( y = 0.5(4) + 1 = 2 + 1 = 3 \)

Completed Table:

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | -0.5| 0 | 0.5| 1 | 1.5| 2 | 2.5| 3 |

---

#### Equation 4: \( y = -x + 3 \)

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | | | | | | | | |

- For \( x = -3 \): \( y = -(-3) + 3 = 3 + 3 = 6 \)
- For \( x = -2 \): \( y = -(-2) + 3 = 2 + 3 = 5 \)
- For \( x = -1 \): \( y = -(-1) + 3 = 1 + 3 = 4 \)
- For \( x = 0 \): \( y = -(0) + 3 = 0 + 3 = 3 \)
- For \( x = 1 \): \( y = -(1) + 3 = -1 + 3 = 2 \)
- For \( x = 2 \): \( y = -(2) + 3 = -2 + 3 = 1 \)
- For \( x = 3 \): \( y = -(3) + 3 = -3 + 3 = 0 \)
- For \( x = 4 \): \( y = -(4) + 3 = -4 + 3 = -1 \)

Completed Table:

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | 6 | 5 | 4 | 3 | 2 | 1 | 0 | -1|

---

#### Equation 5: \( y = -2x - 4 \)

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | | | | | | | | |

- For \( x = -3 \): \( y = -2(-3) - 4 = 6 - 4 = 2 \)
- For \( x = -2 \): \( y = -2(-2) - 4 = 4 - 4 = 0 \)
- For \( x = -1 \): \( y = -2(-1) - 4 = 2 - 4 = -2 \)
- For \( x = 0 \): \( y = -2(0) - 4 = 0 - 4 = -4 \)
- For \( x = 1 \): \( y = -2(1) - 4 = -2 - 4 = -6 \)
- For \( x = 2 \): \( y = -2(2) - 4 = -4 - 4 = -8 \)
- For \( x = 3 \): \( y = -2(3) - 4 = -6 - 4 = -10 \)
- For \( x = 4 \): \( y = -2(4) - 4 = -8 - 4 = -12 \)

Completed Table:

| \( x \) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---------|----|----|----|---|---|---|---|---|
| \( y \) | 2 | 0 | -2 | -4| -6| -8| -10| -12|

---

Final Answer:

\[
\boxed{
\begin{array}{c|ccccccccc}
\text{Equation} & x = -3 & x = -2 & x = -1 & x = 0 & x = 1 & x = 2 & x = 3 & x = 4 \\
\hline
y = 4x - 2 & -14 & -10 & -6 & -2 & 2 & 6 & 10 & 14 \\
y = 3x + 2 & -7 & -4 & -1 & 2 & 5 & 8 & 11 & 14 \\
y = 0.5x + 1 & -0.5 & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\
y = -x + 3 & 6 & 5 & 4 & 3 & 2 & 1 & 0 & -1 \\
y = -2x - 4 & 2 & 0 & -2 & -4 & -6 & -8 & -10 & -12 \\
\end{array}
}
\]