a=3; (* Range of plots *)

Plot[0,{x,-4,4},PlotRange->{{-4,4},{-4,4}},AspectRatio->1,GridLines-> Automatic]

β=0.95;
γ=(1/(Sqrt[1-(β^2)]));

xlines=Table[(((γ x +n))/(γ β)),{n,-3,3}];

Plot[Evaluate[xlines],{x,-4,4},PlotRange->{{-4,4},{-4,4}},AspectRatio->1,GridLines-> Automatic]

tlines=Table[(((γ β x +m))/(γ )),{m,-3,3}]

Plot[Evaluate[tlines],{x,-4,4},PlotRange->{{-4,4},{-4,4}},AspectRatio->1,GridLines->Automatic]

β=0.05`;
γ=(1/(Sqrt[1-(β^2)]))
xlines=Table[((γ x+n)/(γ β)),{n,-3,3}];
tlines=Table[((γ β x+m)/γ),{m,-3,3}];
Plot[Evaluate[Join[tlines,xlines]],{x,-a,a},PlotRange->{{-a,a},{-a,a}},AspectRatio->1,GridLines->Automatic,PlotStyle->Dashing[{0.05`,0.025`}],ImageSize->{6 72,6 72},BaseStyle->{FontSize->14}]