Equation of a Line Parallel to an Axis

Date: 06/19/2003 at 05:45:39
From: Barb
Subject: Slope intercept

How can I get the equation of a line if the line passes through a 
point and is parallel to the x- or y-axis?

Ex: "if the line passes through (-3,-4) and is parallel to the y-axis"

Date: 06/19/2003 at 09:50:11
From: Doctor Ian
Subject: Re: Slope intercept

Hi Barb,

A horizontal line always has an equation that looks like

  y = [some constant]

and a vertical line always has an equation that looks like 

  x = [some constant]

If I know that a horizontal line passes through the point (5,6), then
I know that the value of y is the constant I want, so the equation
must be 

  y = 6

If I know that a vertical line passes through the point, then I need
the value of x instead:

  x = 5

So in fact, we can be a little more precise, and say that a horizontal
line has the equation

  y = [the y-value of any point on the line]

while a vertical line has the equation

  x = [the x-value of any point on the line]

What if you forget these equations? The quickest way to figure them 
out again is to draw a horizontal or vertical line, and start
identifying points on it:

                  x=4
        |          .
        |          .
        |        (4,12)
        |          .
        |          .
        |        (4,9)
        |          .
        |          .
        |          .
     .......(1,3).......(5,3)...........(11,3).....   y=3
        |          .
    ----+----------.-------------------------------
        |          .
        |        (4,-3)
        |          .
        |          .

Does this make sense? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 06/21/2003 at 04:09:56
From: Barb
Subject: Thank you (Slope intercept)

Dr. Ian,

Thank you for your help. I really appreciate this. I now understand 
how to get the line equation. Thanks again!