The line represented by \(x = 7\) is parallel to the x–axis. Justify whether the statement is true or not.
False. \(x = 7\) is a vertical line, hence parallel to the y–axis.
Step 1: Recall the general forms of special lines.
Lines of the form \(x = a\) are vertical lines. They fix the x–coordinate to a constant value and allow the y–coordinate to take any value.
Lines of the form \(y = b\) are horizontal lines. They fix the y–coordinate to a constant value and allow the x–coordinate to vary.
Step 2: Analyze the given line \(x = 7\).
The equation \(x = 7\) means that for every point on this line, the x–coordinate is always 7.
The y–coordinate can take any real value.
Therefore, the line is a vertical line passing through the point \((7, 0)\) on the x–axis.
Step 3: Compare with the coordinate axes.
Vertical lines are parallel to the y–axis, because both extend up and down without changing the x–coordinate.
On the other hand, lines parallel to the x–axis are of the form \(y = b\), which is not the case here.
Conclusion. The line \(x = 7\) is a vertical line, parallel to the y–axis, not the x–axis. Hence, the given statement is false.