Explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
a slope = 0 means that the y coordinate change is always 0, so y does not change anywhere on the line.
that makes y a constant c, and x can be any value completely independent of y.
the line is the summary of all points that have c as their y coordinate.
so, the general equation for such a line is simply
y = c
what is c ?
as we have one point on the line, remember the statement above : the line is the summary of all points that have c as their y coordinate.
that means (3, -4) must have the same y coordinate.
so, c = -4.
the equation of the line is therefore
y = -4