SOLUTION: How do you solve: Write an equation of a line which contains the points (3, -2) and (3,6). Thank you

Let's plot those two points:



Now I will draw a green line through them:




Hmm! That's a very special type of line!

Notice that it is VERICAL.  Vertical lines are the only kinds of lines 
that DO NOT have slopes or y-intercepts!  

However, vertical lines DO have equations.  Notice that the 
two points you were given both have the same x-coordinate 3.

Look at some other points on that vertical line. Five more
points on that line are (3,5), (3,4), (3,2), (3,-3), and (3,-7):



In fact, EVERY point on that line has its x-coordinate
as 3.  

So to describe that vertical green line, we could just say

"The x-coordinate of any point on the line always equals 3"

or

"x always equals 3"

or even shorter

"x = 3"

That's the way to describe a vertical line, just

write "x =" and put whatever number after it

that the x-coordinates of all the points on it are,

in this case all the x-coordinates are 3.

So the equation of that vertical line is

x = 3

You cannot put it in slope-intercept form, 
for two reasons:

1.  It has no slope!

and

2. It has no y-intercept!

So you just have to leave the equation as simply

x = 3

Note:
The problem you have submitted is an unusual kind of problem
because every other kind of line except a vertical line has
a slope and a y-intercept.  All vertical lines have equations 
of the form x = k 

Edwin