Question 365252
my daughter had a problem that i have never seen. Wanting to know if you can explain it to me. (-5,7),(-5,3)
<pre>
I will assume the instructions for the problem was stated this way:

<i><b>Find the equation of the line that passes through the two points
(-5,7) and (-5,3).</i></b>

[If you post again, please state the instructions so we won't have to
guess. Thanks]

Let's plot those two points:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
locate(-5+.2,7+.2,"(-5,7)"), locate(-5+.2,3+.2,"(-5,3)"),
circle(-5,7,.15), circle(-5,3,.15)  )}}}

Now let's draw the line through those points.  I'll draw it in green:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
locate(-5+.2,7+.2,"(-5,7)"), locate(-5+.2,3+.2,"(-5,3)"),
circle(-5,7,.15), circle(-5,3,.15),
green(line(-5,-11,-5,11))

  )}}}

Now let's look at some more points on that same green line.


{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
locate(-5+.2,7+.2,"(-5,7)"), locate(-5+.2,3+.2,"(-5,3)"),
circle(-5,7,.15), circle(-5,3,.15),
green(line(-5,-11,-5,11)),
locate(-5+.2,-3+.2,"(-5,-3)"), circle(-5,-3,.15),
locate(-5+.2,-4+.2,"(-5,-4)"), circle(-5,-4,.15),
locate(-5+.2,5+.2,"(-5,5)"), circle(-5,5,.15),
locate(-5+.2,-9+.2,"(-5,-9)"), circle(-5,-9,.15)

 )}}}

Now take a look at all those points.  

Qestion:  What do all those points have in common?
Answer:   They all have -5 for their x-coordinate.

To make a statement to describe that green vertical line, we would say:

"All the points on that line have the x-coordinate = -5."

In algebra we shorten it to just this:   x = -5  

That's the equation of that green vertical line:

               x = -5

That's all there is to it!

Edwin</pre>