Write the equation of the line that passes through the point (–6, 2) and is parallel to the line whose equation is x = –10, then write the equation of the line that passes through the point (–6, 2) and is perpendicular to the line whose equation is x = –10.

Well x = -10 would create a vertical line, meaning that its slope would be undefined. With that information, you can deduce that the parallel equation you are trying to create would also be vertical. And since you are provided with the detail that said line will pass through (-6,2), all you have to do is write what x would equal, which is -6. So, the first equation will be x = -6.

The second part is slightly more tricky since it calls for a line perpendicular to x = -10, meaning it wants a line that is horizontal. Since you cannot find the negative reciprocal of the term "undefined," you must use your prior knowledge of horizontal lines to deduce that the slope of the wanted line will be 0. Once again, you are given the "passing point" of (-6,2), and using this information you can concur that the line will be perfectly horizontal upon the "2" mark of the y-axis. Therefore, the second equation will be y = 2.

To restate...
First equation: x = -6
Second equation: y = 2

Hope this helps!