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I am trying to add a point in a plot where the curve intercepts the x axis i.e. f[x] = 0 I tried doing an epilog inside an if statement in Plot[] , and it didn't work. here is my code so far

f[pi_, p_] = (10)*(p - pi);
g[p_] = 10*(p);
Manipulate[Plot[{f[pi, p], g[p]}, {p, 0, 50}, PlotLabels -> {"Water & slat", "Pure Water"}, AxesLabel -> {\[CapitalDelta]P, Solvent - Flux}, LabelStyle -> Directive[Bold, Medium],AxesStyle -> Directive[Black], AxesOrigin -> {0, 0}], {pi, 10, 100}, {p, 0, 40}]
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  • $\begingroup$ Instead of an Epilog, you could use the mesh options, e.g., Plot[.., MeshFunctions->{#2&}, Mesh->{{0}}, MeshStyle->Directive[PointSize[Large],Red]] $\endgroup$ – Carl Woll May 23 '17 at 19:29
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f[pi_, p_] = 10*(p - pi);
g[p_] = 10*p;

Clearly, f[pi, p] == 0 for p == pi

Manipulate[
 Plot[{f[pi, p], g[p]}, {p, 0, 100},
  PlotLabels -> {"Water & slat", "Pure Water"},
  AxesLabel -> {ΔP, Solvent - Flux},
  LabelStyle -> Directive[Bold, Medium],
  AxesStyle -> Directive[Black],
  AxesOrigin -> {0, 0},
  Epilog -> {Red, AbsolutePointSize[6],
    Tooltip[Point[{pi, 0}], {pi, 0}]},
  PlotRange -> {{0, 103}, {-1000, 1000}}],
 {{pi, 40}, 10, 100, 1, Appearance -> "Labeled"}]

enter image description here

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