Graph the equations on the coordinate planes. $$ x=6 $$

Question

UpStudy AI · Accepted Answer

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
 |
 |
 |                     
 |                     
 |                     
 |                     
 |                     
 |                     
 |                     
 |------------------------ x
                 |
                 |
                 |
                 |
                 |
                 |
                 |
                 |
                 |
                 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.
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).

Graph the equations on the coordinate planes.

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Solución

Understanding the Equation

Graphing

Visual Representation

Plotting Points

Conclusion

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