Question
Graph the equations on the coordinate planes. \( x=6 \)
Ask by Tucker Maxwell. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The graph of \( x = 6 \) is a vertical line that runs parallel to the y-axis and intersects the x-axis at the point (6, 0).
Solution
Certainly! Let's graph the equation \( x = 6 \) on a 2D coordinate plane.
## Understanding the Equation \( x = 6 \)
The equation \( x = 6 \) represents all points in the Cartesian plane where the **x-coordinate** is always **6**, regardless of the y-coordinate. This means that for every point on this graph, the horizontal position is fixed at 6, and the vertical position can be any real number.
## Graphing \( x = 6 \)
Since \( x = 6 \) doesn't depend on \( y \), its graph is a **vertical line** that crosses the x-axis at the point (6, 0). This line extends infinitely in both the positive and negative directions along the y-axis.
### Visual Representation
Here's a simple ASCII representation of the graph:
```
y
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|------------------------ x
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6
```
- **Vertical Line at \( x = 6 \):** The vertical line runs parallel to the y-axis and intersects the x-axis at \( x = 6 \).
### Plotting Points
To better understand, let's list some points that lie on the line \( x = 6 \):
| x | y |
|---|----|
| 6 | -3 |
| 6 | -2 |
| 6 | -1 |
| 6 | 0 |
| 6 | 1 |
| 6 | 2 |
| 6 | 3 |
| ... | ... |
All these points have an x-coordinate of 6 but can have any y-coordinate.
## Conclusion
- **Type of Graph:** Vertical Line
- **Slope:** Undefined (since vertical lines have no slope)
- **Intercept:** Intersects the x-axis at (6, 0)
This line represents all possible points where the x-value is consistently 6 across the entire y-axis.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
The equation \( x = 6 \) represents a vertical line on the coordinate plane. This line consists of all points where the x-coordinate is 6, regardless of the y-coordinate. So, you'll find points like (6, 0), (6, 1), (6, -3), and so on, all stacked vertically. Just draw a straight line parallel to the y-axis that crosses the x-axis at 6—easy peasy! Now, you can think of this line as a boundary—say, in a real-world application. For example, if you're building a fence and the property begins at \( x = 6 \), any structures or garden plots you plan would need to stay to the right of that line, illustrating how math helps to define spaces in our world!
