Graphing Horizontal and Vertical Lines Worksheets - Free Printable

Let's solve each of these problems step by step. The task is to graph horizontal and vertical lines based on their equations.

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🔍 Key Concepts:

- Vertical lines: These are lines where the x-value is constant (doesn't change).
Equation form: $ x = a $
→ This line goes straight up and down, passing through all points where $ x = a $, regardless of $ y $.

- Horizontal lines: These are lines where the y-value is constant (doesn't change).
Equation form: $ y = b $
→ This line goes straight left and right, passing through all points where $ y = b $, regardless of $ x $.

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Now let’s go through each problem:

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1) $ x = 7 $

- This is a vertical line.
- It passes through all points where $ x = 7 $, no matter what $ y $ is.
- So, draw a vertical line that intersects the x-axis at 7.

✔ Graph: Draw a straight vertical line going up and down through $ x = 7 $.

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2) $ y = -8 $

- This is a horizontal line.
- It passes through all points where $ y = -8 $, regardless of $ x $.
- So, draw a horizontal line that intersects the y-axis at -8.

✔ Graph: Draw a straight horizontal line going left and right through $ y = -8 $.

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3) $ y = 0 $

- This is a horizontal line.
- $ y = 0 $ means it lies along the x-axis.
- Every point on this line has $ y = 0 $.

✔ Graph: Draw the x-axis itself — a horizontal line passing through the origin.

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4) $ x = 9 $

- This is a vertical line.
- It passes through all points where $ x = 9 $.
- So, draw a vertical line intersecting the x-axis at 9.

✔ Graph: Draw a vertical line through $ x = 9 $.

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5) $ x = -15 $

- Vertical line.
- Passes through $ x = -15 $, so far to the left of the origin.
- Draw a vertical line intersecting the x-axis at -15.

✔ Graph: A vertical line at $ x = -15 $.

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6) $ y = 5 $

- Horizontal line.
- Passes through all points where $ y = 5 $.
- Draw a horizontal line crossing the y-axis at 5.

✔ Graph: A horizontal line at $ y = 5 $.

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✔ Summary of Graphs:

| Equation | Type | Description |
|--------------|------------|-------------|
| $ x = 7 $ | Vertical | Line at $ x = 7 $ |
| $ y = -8 $ | Horizontal | Line at $ y = -8 $ |
| $ y = 0 $ | Horizontal | The x-axis |
| $ x = 9 $ | Vertical | Line at $ x = 9 $ |
| $ x = -15 $ | Vertical | Line at $ x = -15 $ |
| $ y = 5 $ | Horizontal | Line at $ y = 5 $ |

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📌 How to Sketch Each:

For each graph:
- Locate the value on the appropriate axis.
- Draw a straight line perpendicular to that axis:
- For $ x = \text{constant} $ → vertical line
- For $ y = \text{constant} $ → horizontal line

> Example: For $ x = 7 $, find 7 on the x-axis, then draw a straight vertical line upward and downward.

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Final Answer (Instructions for Graphing):

1. $ x = 7 $: Vertical line through $ x = 7 $
2. $ y = -8 $: Horizontal line through $ y = -8 $
3. $ y = 0 $: The x-axis
4. $ x = 9 $: Vertical line through $ x = 9 $
5. $ x = -15 $: Vertical line through $ x = -15 $
6. $ y = 5 $: Horizontal line through $ y = 5 $

You can now sketch these on the provided grids accordingly.

Let me know if you'd like a visual description or help labeling the graphs!