Write an equation for the line described. Write the equation in the form specified. 11) parallel to \( x=6 \), through \( (7,2) \) \( \begin{array}{llll}\text { A) } x=2 & \text { B) } y=6 & \text { C) } y=2 & \text { D) } x=7\end{array} \)

To write the equation for a line that is parallel to \( x=6 \) and goes through the point \( (7,2) \), we first need to remember that lines parallel to a vertical line (like \( x=6 \)) are also vertical. Therefore, the equation of the line will be of the form \( x = k \), where \( k \) is the x-coordinate of the given point. In this case, since it goes through \( (7, 2) \), the equation will be \( x = 7 \). So, the answer is \( x=7 \), which corresponds to option D. For a fun twist: Just think of it this way – if you're at a carnival funhouse, the vertical mirrors on either side of you are like parallel lines. No matter how much you move around, those mirrors (or your new line) stay vertical too! And speaking of equations, did you know that every vertical line can be crossed by horizontal roads? In mathematical terms, that means you can always find perpendicular lines (like \( y=2 \), which would be horizontal through your point). Vertical lines, like the one you just created, have no slopes and simply run straight up and down, which is a unique aspect worthy of a celebration!