To find the equation of the line passing through the given points [tex]\( S\left(\frac{1}{2}, 1\right) \)[/tex] and [tex]\( T\left(\frac{1}{2}, 4\right) \)[/tex], follow these steps:
1. Identify the coordinates of the points:
- [tex]\( S\left(\frac{1}{2}, 1\right) \)[/tex]
- [tex]\( T\left(\frac{1}{2}, 4\right) \)[/tex]
2. Determine the type of line:
- Notice that both points have the same x-coordinate, [tex]\( \frac{1}{2} \)[/tex].
- When both points have the same x-coordinate, the line passing through these points is a vertical line.
3. Formulate the equation of a vertical line:
- For any vertical line, the equation is of the form [tex]\( x = a \)[/tex], where [tex]\( a \)[/tex] is the constant x-coordinate through which the line passes.
4. Substitute the x-coordinate:
- Since the common x-coordinate for both points [tex]\( S \)[/tex] and [tex]\( T \)[/tex] is [tex]\( \frac{1}{2} \)[/tex]:
- The equation of the line is [tex]\( x = \frac{1}{2} \)[/tex].
Therefore, the equation of the line in standard form is:
[tex]\[ \boxed{x = \frac{1}{2}} \][/tex]
This matches the second provided choice from the given options.
