points =Table[{x+(Random[]-.5),x/2+12(Random[]-.5)(Random[]-.5)},{x,-3.5,3.5,.07}];

Manipulate[Show[Graphics[{If[distances,Gray,White],Line[{#,{#[[1]],m#[[1]]}}]&/@points,Red,Thick,Line[{{-5,-5m},{5,5m}}],Blue,PointSize[.015],Point/@points}],Axes->True,PlotRange->{{-5,5},{-4,6}}],{m,-3,3},{distances,{False,True}}]