Drawing Straight-Line Graphs worksheet with four linear equations and corresponding coordinate grids for graphing.

Problem Overview:

The task involves drawing straight-line graphs for the given linear equations. To do this, we need to:
1. Calculate the corresponding \( y \)-values for each given \( x \)-value using the equation.
2. Plot the points on the graph.
3. Draw a straight line through these points.

The equations provided are:
1. \( y = 2x + 1 \)
2. \( y = 3x - 1 \)
3. \( y = x + 5 \)
4. \( y = 2x - 5 \)
5. \( y = x - 3 \)
6. \( y = 4x + 7 \)

For each equation, the \( x \)-values are given as: \( -3, -2, -1, 0, 1, 2, 3 \).

---

Step-by-Step Solution:

#### 1. Equation: \( y = 2x + 1 \)

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

- For \( x = -3 \): \( y = 2(-3) + 1 = -6 + 1 = -5 \)
- For \( x = -2 \): \( y = 2(-2) + 1 = -4 + 1 = -3 \)
- For \( x = -1 \): \( y = 2(-1) + 1 = -2 + 1 = -1 \)
- For \( x = 0 \): \( y = 2(0) + 1 = 0 + 1 = 1 \)
- For \( x = 1 \): \( y = 2(1) + 1 = 2 + 1 = 3 \)
- For \( x = 2 \): \( y = 2(2) + 1 = 4 + 1 = 5 \)
- For \( x = 3 \): \( y = 2(3) + 1 = 6 + 1 = 7 \)

Completed table:
| \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | \( 2 \) | \( 3 \) |
|---------|----------|----------|----------|---------|---------|---------|---------|
| \( y \) | \( -5 \) | \( -3 \) | \( -1 \) | \( 1 \) | \( 3 \) | \( 5 \) | \( 7 \) |

Graph: Plot the points \( (-3, -5) \), \( (-2, -3) \), \( (-1, -1) \), \( (0, 1) \), \( (1, 3) \), \( (2, 5) \), and \( (3, 7) \). Draw a straight line through these points.

---

#### 2. Equation: \( y = 3x - 1 \)

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

- For \( x = -3 \): \( y = 3(-3) - 1 = -9 - 1 = -10 \)
- For \( x = -2 \): \( y = 3(-2) - 1 = -6 - 1 = -7 \)
- For \( x = -1 \): \( y = 3(-1) - 1 = -3 - 1 = -4 \)
- For \( x = 0 \): \( y = 3(0) - 1 = 0 - 1 = -1 \)
- For \( x = 1 \): \( y = 3(1) - 1 = 3 - 1 = 2 \)
- For \( x = 2 \): \( y = 3(2) - 1 = 6 - 1 = 5 \)
- For \( x = 3 \): \( y = 3(3) - 1 = 9 - 1 = 8 \)

Completed table:
| \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | \( 2 \) | \( 3 \) |
|---------|----------|----------|----------|---------|---------|---------|---------|
| \( y \) | \( -10 \)| \( -7 \) | \( -4 \) | \( -1 \)| \( 2 \) | \( 5 \) | \( 8 \) |

Graph: Plot the points \( (-3, -10) \), \( (-2, -7) \), \( (-1, -4) \), \( (0, -1) \), \( (1, 2) \), \( (2, 5) \), and \( (3, 8) \). Draw a straight line through these points.

---

#### 3. Equation: \( y = x + 5 \)

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

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

Completed table:
| \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | \( 2 \) | \( 3 \) |
|---------|----------|----------|----------|---------|---------|---------|---------|
| \( y \) | \( 2 \) | \( 3 \) | \( 4 \) | \( 5 \) | \( 6 \) | \( 7 \) | \( 8 \) |

Graph: Plot the points \( (-3, 2) \), \( (-2, 3) \), \( (-1, 4) \), \( (0, 5) \), \( (1, 6) \), \( (2, 7) \), and \( (3, 8) \). Draw a straight line through these points.

---

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

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

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

Completed table:
| \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | \( 2 \) | \( 3 \) |
|---------|----------|----------|----------|---------|---------|---------|---------|
| \( y \) | \( -11 \)| \( -9 \) | \( -7 \) | \( -5 \)| \( -3 \)| \( -1 \)| \( 1 \) |

Graph: Plot the points \( (-3, -11) \), \( (-2, -9) \), \( (-1, -7) \), \( (0, -5) \), \( (1, -3) \), \( (2, -1) \), and \( (3, 1) \). Draw a straight line through these points.

---

#### 5. Equation: \( y = x - 3 \)

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

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

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

Graph: Plot the points \( (-3, -6) \), \( (-2, -5) \), \( (-1, -4) \), \( (0, -3) \), \( (1, -2) \), \( (2, -1) \), and \( (3, 0) \). Draw a straight line through these points.

---

#### 6. Equation: \( y = 4x + 7 \)

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

- For \( x = -3 \): \( y = 4(-3) + 7 = -12 + 7 = -5 \)
- For \( x = -2 \): \( y = 4(-2) + 7 = -8 + 7 = -1 \)
- For \( x = -1 \): \( y = 4(-1) + 7 = -4 + 7 = 3 \)
- For \( x = 0 \): \( y = 4(0) + 7 = 0 + 7 = 7 \)
- For \( x = 1 \): \( y = 4(1) + 7 = 4 + 7 = 11 \)
- For \( x = 2 \): \( y = 4(2) + 7 = 8 + 7 = 15 \)
- For \( x = 3 \): \( y = 4(3) + 7 = 12 + 7 = 19 \)

Completed table:
| \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | \( 2 \) | \( 3 \) |
|---------|----------|----------|----------|---------|---------|---------|---------|
| \( y \) | \( -5 \) | \( -1 \) | \( 3 \) | \( 7 \) | \( 11 \)| \( 15 \)| \( 19 \)|

Graph: Plot the points \( (-3, -5) \), \( (-2, -1) \), \( (-1, 3) \), \( (0, 7) \), \( (1, 11) \), \( (2, 15) \), and \( (3, 19) \). Draw a straight line through these points.

---

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{See the step-by-step calculations and graphs above.}
\end{array}
}
\]