Making a secant line slide along a curve with Manipulate

Question

I need to create a slider that displays the secant line of the function (defined as functionsecant) using the Manipulate function in mathematica, but I can't get it to work and I can't find any tutorials breaking down how the function works and how your supposed to put in input. (I am brand new to Mathematica)

This is what I thought would work, but apparently it doesn't.

Manipulate[
 Plot[function[x], functionsecant[x], {x, -10, 10}, 
  PlotRange -> {{-5, 5}, {-5, 5}}, 
  Epilog -> {Red, PointSize[.015], Point@{p, functionsecant[p]}}], {p, 0, 
  10}]

And it's supposed to plot the secant line from (0,0) to (a,f(a)). How exactly do I do this? I'm at my wit's end D:

Answer 1

You're not too far off. First, if you want to plot multiple functions, they should be surrounded by curly braces {function[x], functionsecant[x]}. Second, unless I'm missing something, I don't think you need functionsecant. If you get rid of functionsecant and turn the functionsecant[p] in your Epilog to function[p], you should end up with a red dot that indicates the end position of your secant line.

You can turn this into a line by adding Line[{{0, 0}, {p, function[p]}}] into your Epilog. Here's an example to help you out:

function[x_] := Sin[x]
Manipulate[
 Plot[
  function[x],
  {x, 0, 8 \[Pi]},
  Epilog -> {
    Line[{{0, 0}, {a, function[a]}}],
    Red,
    Point@{{0, 0}, {a, function[a]}}
    }
  ],
 {a, 0, 8 \[Pi]}]