The segment from (3, 0) to (4, -1) has "x range" 4- 2= 1 and "y range" -1- 0= -1: that is, to go from (3, 0) to (4, -1) you go to the right 1 and down 1. The "slope" is -1/1= -1. If you extend that line past (4, -1) you have to keep that same slope so you extend to the right some distance x and down that same distance: y= -x. Of course the distance is given by and, since y= -x, that is . Add to 4 and subtract it from 1 to get the (x,y) coordinates of the endpoint in that direction. Go the other way, past (3,0) to get the other endpoint.