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A quick Note on Line parallel to a axis:
We know the equation of a line is ax+by+c=0 where c is a constant and the slope is (coeff of x/Co-eff of y).
y=c, a constant, is the equation of any line parallel to x axis (horizontal line) and x=c, a constant is the equation fo any line parallel to y axis (vertical line). The slope of ALL horizontal lines = 0 and the slope of ALL vertical lines is UNDEFINED.