Question 129845
Horizontal lines have points where the y-coordinates are identical for every point in the line, and the x-coordinates can be any real number.  They also have a zero slope, so {{{y=mx+b}}} makes sense.  Since all of the points have the same y-coordinate, the y-intercept must be (0,7), and then the equation would be {{{y=0x+7}}}, or just {{{y=7}}}


Vertical lines are unique in that the slope is undefined, so {{{y=mx+b}}} doesn't make any sense.  However, vertical lines are similar to horizontal lines except that it is the x-coordinate that remains constant and the y-coordinate can be any real number.  So the equation is {{{x=-3}}}, which is another way of saying, "I don't care what y is, as long as x is -3."  Of course, you could make a similar descriptive statement for your vertical line.


Both of these equations are in standard form, because standard form is {{{Ax+By=C}}}.  In the case of the horizontal line, A = 0, B = 1, and C = 7.  In the case of your vertical line, A = 1, B = 0, and C = -3, and the terms with 0 coefficients simply go away, although you could actually write them out like so:

For your vertical line:  {{{0x + y = 7}}}.  However, that is trivial silliness.