How to write a equation of a line that passes through a given point and is parallel and/or perpendicular to the x-axis and/or y-axis

Question

I'm having trouble figuring out how to do this and I feel that if I know how to solve one of the parallel or perpendicular I can figure out the other one so the example I had was

What is the equation of a line that passes through the point (7,9) and is perpendicular to the x-axis?

I can never figure out how to find this when I don't have graph paper can someone please help me. It would be greatly appreciated.

Thank You

Answer 1

The x-axis is a horizontal line. A line perpendicular to a horizontal line is a vertical line.

All vertical lines fit the form of x = __ (some number) for instance x = 4 is a vertical line that goes through (4, 0) or (4, 2) or (4, -10). See how it works? The x-coordinate is always 4 and the y-coordinate can be any value. That's what makes it a vertical line.

In this case, you are looking for a vertical line that goes through (7, 9) which means the x-value is 7. Can you find the equation then?

By the way, a horizontal line will always fit the form y = __ (some number) so the horizontal line that goes through the point (2, 7) is y = 7

Answer 2

Any line perpendicular to the x-axis will be written in x = k form (unlike most other lines in HS geometry which are written in y = mx + b form).

So the answer to this question is the line x = 7 is perpendicular to the x-axis and passes through (7, 9). In fact, the line x = 7 passes through all points where x is equal to 7 in the ordered pair (x, y). In layman's terms the line x = 7 is a vertical line where the x is always 7 and thus (7, y) will always be on that line (where y here is a variable meaning any positive or negative real number).

Hope this helps.