Question 29359
Determine the equation of the following line. Write the answer in standard form using only integers  as coefficients.:
…..The line through (-2,  4) that is perpendicular to the x-axis.

The line through (-2,  4) that is perpendicular to the x-axis.
Any line perpendicular to the x-axis is parallel to the y-axis
And any line parallel to the y -axis has its equation by
x= k   ----(1)
Now P(-2,4) is a point on this line
Therefore putting x=-2 in (1)
(-2) =k
That is k=-2  (*)
Putting (*) in (1)
the required equation is 
x=-2
which is a line parallel to the y-axis at a distance 2 units to the left of it

Note: In the above because you do not find any y in the equation (1) you did n't have the opportunity to supply y=4 in the equation to the line. This matter should not leave you perplexed. If that 4 is still disturbing,draw the co-ordinate axes of reference,draw a line parallel to the y-axis at a distance 2 units to the left of the origin.Mark the point P on this vertical line by going 4 units above the x-axis. You reach the point P(-2,4)
Mark any other point or points on this vertical line. all of them will have their x-coordinate given by (-2). Hence the equation to that line is identified by x=-2
Therefore the general rule of thumb is :
Any line parallel to the x-axis will have its equation given by
y= c
where c is the distance between our line and the x-axis
If c >0 that is if c is positive, then the line is above the x-axis
If C <0 that is if c is negative,then the line is below the x-axis
Any line parallel to the y-axis will have its equation given by
x= k
where k is the distance between our line and the y-axis
If k >0 that is if k is positive, then the line is to the right of the y-axis
If k <0 that is if k is negative,then the line is to the left of the y-axis

Note: If you had thought along the lines of slope and one point form of equation to the line there is no harm!
Any line perpendicular to the x-axis makes an angle 90 degrees 
with the x-axis and has slope = tan(90)= infinity = (something)/0
The slope and one point form of equation to a line is
(y-y1)/(x-x1) = slope where P(x1,y1) is the given fixed point
And here P(x1,y1)=P(-2,4)
Therefore applying the above equation
(y-4)/([x-(-2)] =(something)/0
which implies the dr = 0 
Therefore [x-(-2)] =0
x+2 = 0
That is x= -2  
Note:(If a fraction is zero,then the nr =0 
and if a fraction is infinity then the dr = 0)