Use function machines to find coordinates and plot lines for linear functions.

Problem Overview:

The task involves using function machines to generate coordinates for three different linear functions and then plotting these points on a graph. The functions are:

1. \( y = x + 1 \)
2. \( y = x + 3 \)
3. \( y = 2x \)

For each function, we need to calculate the corresponding \( y \)-values for given \( x \)-values (0, 1, 2, 3) and then plot the resulting coordinates on the provided graphs.

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Step-by-Step Solution:

#### Function 1: \( y = x + 1 \)

1. Given Function: \( y = x + 1 \)
2. Calculate \( y \)-values for \( x = 0, 1, 2, 3 \):
- For \( x = 0 \): \( y = 0 + 1 = 1 \) → Coordinate: \( (0, 1) \)
- For \( x = 1 \): \( y = 1 + 1 = 2 \) → Coordinate: \( (1, 2) \)
- For \( x = 2 \): \( y = 2 + 1 = 3 \) → Coordinate: \( (2, 3) \)
- For \( x = 3 \): \( y = 3 + 1 = 4 \) → Coordinate: \( (3, 4) \)

3. Coordinates Table:
| \( x \) | \( y = x + 1 \) | Coordinates |
|---------|------------------|-------------|
| 0 | 1 | (0, 1) |
| 1 | 2 | (1, 2) |
| 2 | 3 | (2, 3) |
| 3 | 4 | (3, 4) |

4. Plotting Points:
- Plot the points \( (0, 1) \), \( (1, 2) \), \( (2, 3) \), and \( (3, 4) \) on the graph.
- Draw a straight line through these points.

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

1. Given Function: \( y = x + 3 \)
2. Calculate \( y \)-values for \( x = 0, 1, 2, 3 \):
- For \( x = 0 \): \( y = 0 + 3 = 3 \) → Coordinate: \( (0, 3) \)
- For \( x = 1 \): \( y = 1 + 3 = 4 \) → Coordinate: \( (1, 4) \)
- For \( x = 2 \): \( y = 2 + 3 = 5 \) → Coordinate: \( (2, 5) \)
- For \( x = 3 \): \( y = 3 + 3 = 6 \) → Coordinate: \( (3, 6) \)

3. Coordinates Table:
| \( x \) | \( y = x + 3 \) | Coordinates |
|---------|------------------|-------------|
| 0 | 3 | (0, 3) |
| 1 | 4 | (1, 4) |
| 2 | 5 | (2, 5) |
| 3 | 6 | (3, 6) |

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

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#### Function 3: \( y = 2x \)

1. Given Function: \( y = 2x \)
2. Calculate \( y \)-values for \( x = 0, 1, 2, 3 \):
- For \( x = 0 \): \( y = 2 \cdot 0 = 0 \) → Coordinate: \( (0, 0) \)
- For \( x = 1 \): \( y = 2 \cdot 1 = 2 \) → Coordinate: \( (1, 2) \)
- For \( x = 2 \): \( y = 2 \cdot 2 = 4 \) → Coordinate: \( (2, 4) \)
- For \( x = 3 \): \( y = 2 \cdot 3 = 6 \) → Coordinate: \( (3, 6) \)

3. Coordinates Table:
| \( x \) | \( y = 2x \) | Coordinates |
|---------|--------------|-------------|
| 0 | 0 | (0, 0) |
| 1 | 2 | (1, 2) |
| 2 | 4 | (2, 4) |
| 3 | 6 | (3, 6) |

4. Plotting Points:
- Plot the points \( (0, 0) \), \( (1, 2) \), \( (2, 4) \), and \( (3, 6) \) on the graph.
- Draw a straight line through these points.

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Final Answer:

The coordinates and their respective plots are as follows:

1. For \( y = x + 1 \):
- Coordinates: \( (0, 1) \), \( (1, 2) \), \( (2, 3) \), \( (3, 4) \)
- Plot these points and draw a line.

2. For \( y = x + 3 \):
- Coordinates: \( (0, 3) \), \( (1, 4) \), \( (2, 5) \), \( (3, 6) \)
- Plot these points and draw a line.

3. For \( y = 2x \):
- Coordinates: \( (0, 0) \), \( (1, 2) \), \( (2, 4) \), \( (3, 6) \)
- Plot these points and draw a line.

\[
\boxed{
\begin{array}{c}
\text{For } y = x + 1: (0, 1), (1, 2), (2, 3), (3, 4) \\
\text{For } y = x + 3: (0, 3), (1, 4), (2, 5), (3, 6) \\
\text{For } y = 2x: (0, 0), (1, 2), (2, 4), (3, 6)
\end{array}
}
\]