Question 315771
Write an equation of the line which passes through these points

(0, -4) and (0, 8)
<pre><b>

Let's plot those two points:

{{{drawing(400, 400,-10,10,-10,10,
locate(-.4,-3.62,"@"),locate(-.1,-3.62,"@"),
line(-.2,-4,.2,-4), line(-.2,8,.2,8),
locate(-.4,8.3,"@"),locate(-.1,8.3,"@"),
locate(0.2,-4+.3,"(0,-4)"), locate(0.2,8+.3,"(0,8)"), 
graph(400,400,-10,10,-10,10) )}}}

As you see those two points are on the y-axis, so if we connect
them, the line will coincide with the y-axis -- in fact the line 
IS the y-axis.  So we want the equation of the y-axis.  Look at 
a couple more points on that line, the y-axis, say (0,5) and (0,-7). 

{{{drawing(400, 400,-10,10,-10,10,
locate(-.4,-3.62,"@"),locate(-.1,-3.62,"@"),
line(-.2,-4,.2,-4), line(-.2,8,.2,8), green(line(0,-11,0,11)),
locate(-.4,5.3,"@"),locate(-.1,5.3,"@"), locate(0.2,5+.3,"(0,5)"),
locate(-.4,-7+.3,"@"),locate(-.1,-7+.3,"@"), locate(0.2,-7+.3,"(0,-7)"),
graph(400,400,-10,10,-10,10),
locate(0.2,-4+.3,"(0,-4)"), locate(0.2,8+.3,"(0,8)") )}}}

Notice that all those point have 0 for their x-coordinate.  Every point
on the y-axis has its x-coordinate 0, so the way the equation is made
is to state that fact in an equation about all the x-coordinates being
0.  The equation that says that is:

     x = 0

That is the equation of the y-axis, because every point on the y-axis
has its x coordinate as 0.

Edwin</pre>