We can write y=mx+c where m=slope and c is the y intercept for amy pair of points. If the same equation fits all three points the points are collinear. m=(14-(-4))/(3-1)=(5-14)/(2-3)=(5-(-4))/(2-1)=9, This is sufficient to prove they are collinear.
So y=9x+c and 5=18+c, c=-13, y=9x-13. Plug in each point and you will find the equation is satisfied for each point.