You get a graph like that with
f[x_] := (3 x - 1)/(2 x + 6);
Plot[{f[x], 3/2}, {x, -11, 7}, Exclusions -> {x == -3},
ExclusionsStyle -> Red, PlotStyle -> {Black, Red}, PlotRange -> 10,
AspectRatio -> Automatic]
You can insert the labels with Epilog:
f[x_] := (3 x - 1)/(2 x + 6);
Plot[{f[x], 3/2}, {x, -11, 7}, Exclusions -> {x == -3},
ExclusionsStyle -> Red, PlotStyle -> {Black, Red}, PlotRange -> 10,
AspectRatio -> Automatic,
Epilog -> {Text[x == -3, {-5, -8}], Text[y == 1.5, {5, 2}]}]
