Graph the equations on the coordinate planes. \( x=6 \)

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.