The equation of a line in explicit form is:
y=mx+q, where m is the slope and q the y-intercept.
It is easier to show the procedure with some example:
y=2: this line is parallel to the x-axis and it passes from the point P(0,2).
x=3: this line is parallel to the y-axis and it passes from the point P(2,0).
y=x+1: this line is parallel to the bisector of the I and III quadrants and it passes from the point P(0,1).
graph{x+1 [-10, 10, -5, 5]}
y=-x-1: this line is parallel to the bisector of the II and IV quadrants and it passes from the point P(0,-1).
graph{-x-1 [-10, 10, -5, 5]}
y=2/3x+1: we have to find the point P(0,1), from this point we have to "count" 3 units to the right and then 2 units to the up, so we can find the point #Q(3,3), then we have to join the two point found.
graph{2/3x+1 [-10, 10, -5, 5]}
y=-1/2x-1: we have to find the point P(0,-1), from this point we have to "count" 2 units to the left and then 2 units to the up, so we can find the point #Q(-2,0), then we have to join the two point found.
graph{-1/2x-1 [-10, 10, -5, 5]}
The difference in these two last examples is the "choice" of the "right" and the "left". Right, if the m is positive; left, if the m is negative.
