Linear Functions (A) Worksheet | 8th Grade PDF Worksheets - Free Printable

Problem Analysis:

The worksheet involves plotting linear functions on a coordinate plane and identifying intersection points. Let's break it down into sections:

---

#### Section A: Plot and Label the Functions
We are given several equations to plot:
1. \( y = 3 \)
2. \( x = 2 \)
3. \( y = -3 \)
4. \( x = 1 \)
5. \( y = 6 \)
6. \( x = 0 \)
7. \( y = 0 \)
8. \( x = -6 \)

These are all vertical or horizontal lines. We need to plot them on the provided grid and find the coordinates of their intersections.

##### Step 1: Plotting the Lines
- \( y = 3 \): This is a horizontal line passing through \( y = 3 \).
- \( x = 2 \): This is a vertical line passing through \( x = 2 \).
- \( y = -3 \): This is a horizontal line passing through \( y = -3 \).
- \( x = 1 \): This is a vertical line passing through \( x = 1 \).
- \( y = 6 \): This is a horizontal line passing through \( y = 6 \).
- \( x = 0 \): This is the y-axis.
- \( y = 0 \): This is the x-axis.
- \( x = -6 \): This is a vertical line passing through \( x = -6 \).

##### Step 2: Finding Intersection Points
We need to find the intersection points of the following pairs:
1. \( x = 2 \) and \( y = 3 \)
2. \( x = 2 \) and \( y = -3 \)
3. \( x = 1 \) and \( y = 6 \)
4. \( x = -6 \) and \( y = 0 \)

- Intersection of \( x = 2 \) and \( y = 3 \):
- The point where \( x = 2 \) and \( y = 3 \) is \( (2, 3) \).

- Intersection of \( x = 2 \) and \( y = -3 \):
- The point where \( x = 2 \) and \( y = -3 \) is \( (2, -3) \).

- Intersection of \( x = 1 \) and \( y = 6 \):
- The point where \( x = 1 \) and \( y = 6 \) is \( (1, 6) \).

- Intersection of \( x = -6 \) and \( y = 0 \):
- The point where \( x = -6 \) and \( y = 0 \) is \( (-6, 0) \).

##### Final Answer for Section A
\[
\begin{array}{|c|c|c|}
\hline
x & y & \text{Coordinates of intersection} \\
\hline
x = 2 & y = 3 & (2, 3) \\
\hline
x = 2 & y = -3 & (2, -3) \\
\hline
x = 1 & y = 6 & (1, 6) \\
\hline
x = -6 & y = 0 & (-6, 0) \\
\hline
\end{array}
\]

---

#### Section B: Plot and Label Each Function
We are given the function \( y = x \) and need to plot it by finding coordinates for specific \( x \)-values.

##### Step 1: Calculate Coordinates
For \( y = x \):
- When \( x = -1 \), \( y = -1 \). Coordinates: \( (-1, -1) \)
- When \( x = 0 \), \( y = 0 \). Coordinates: \( (0, 0) \)
- When \( x = 1 \), \( y = 1 \). Coordinates: \( (1, 1) \)
- When \( x = 2 \), \( y = 2 \). Coordinates: \( (2, 2) \)
- When \( x = 3 \), \( y = 3 \). Coordinates: \( (3, 3) \)
- When \( x = 4 \), \( y = 4 \). Coordinates: \( (4, 4) \)

##### Step 2: Plot the Points
Plot the points \( (-1, -1) \), \( (0, 0) \), \( (1, 1) \), \( (2, 2) \), \( (3, 3) \), and \( (4, 4) \) on the grid and draw a straight line through them.

##### Final Answer for Section B
\[
\begin{array}{|c|c|c|}
\hline
x & y = x & \text{Coordinates} \\
\hline
-1 & -1 & (-1, -1) \\
\hline
0 & 0 & (0, 0) \\
\hline
1 & 1 & (1, 1) \\
\hline
2 & 2 & (2, 2) \\
\hline
3 & 3 & (3, 3) \\
\hline
4 & 4 & (4, 4) \\
\hline
\end{array}
\]

---

Final Answers

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
x & y & \text{Coordinates of intersection} \\
\hline
x = 2 & y = 3 & (2, 3) \\
\hline
x = 2 & y = -3 & (2, -3) \\
\hline
x = 1 & y = 6 & (1, 6) \\
\hline
x = -6 & y = 0 & (-6, 0) \\
\hline
\end{array}
}
\]
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
x & y = x & \text{Coordinates} \\
\hline
-1 & -1 & (-1, -1) \\
\hline
0 & 0 & (0, 0) \\
\hline
1 & 1 & (1, 1) \\
\hline
2 & 2 & (2, 2) \\
\hline
3 & 3 & (3, 3) \\
\hline
4 & 4 & (4, 4) \\
\hline
\end{array}
}
\]