The only way that 2 lines don't intersect is when they are paralell the only time 2 lines that are straight are paralell, is when the slopes are the same find the slopes
slope=(y1-y2)/(x1-x2) so the points of the line (0,-1) and (2,3) are y1=-1 y2=3 x1=0 x2=2 so subsitute (-1-3)/(0-2)=-4/-2=4/2=2 slope=2
the ohter one points (-2,4) and (-3,3) y1=4 y2=3 x1=-2 x2=-3 subsitute (4-3)/(-2-(-3))=1/(-2+3)=1/1=1 slope=1