which equation represents the vertical line passing through (3, -5)?

Answer 1

There are two important pieces of information: The graph must pass through the point (3,-5), and it must be a vertical line. For the second piece, we recall the general form of a vertical line is of the form x = c, for some real number constant c. This is the case because a vertical line realizes every y value, thus there is no data in the y coordinate, and has a single fixed x value, determining where the vertical line is located in the plane R^2.

Then to pick a real number constant c, we use the first piece of information, which is that the point must pass through (3,-5). Plugging this point into our general equation, we have 3 = c, thus the equation defining the line is x = 3.