Display div if option is selected in jQuery

Question

I am trying to display a div if one of 2 options is selected on my page. Here is the select menu:

<select id="graph_select">
<option id="pilot_form">Pilot Hours</option>
<option id="client_form">Client Hours</option>
</select>

Here is my first div for the first option:

<div id="pilot_graph_form" align="center" style="margin:0 auto; display:none;">
        <form action="?page=reporter" method="POST" name="graph_form">
            <p>From:</p>
            <select name="start_date">
                <cfloop query="date_worked_menu">
                    <option>#date_worked_menu.date_worked#</option>
                </cfloop>
            </select>
            <br />
            <br />
            <p>To:</p>
            <select name="end_date">
                <cfloop query="date_worked_menu">
                    <option>#date_worked_menu.date_worked#</option>
                </cfloop>   
            </select>
            <br />
            <input class="btn btn-success" type="Submit" name="submit_to_graph" value="Submit" id="submit_to_graph">
        </form>
    </div>

Here is the div for my second option:

<div id="client_graph_form" align="center" style="margin:0 auto; display:none;">
        <form action="?page=reporter" method="POST" name="graph_form_clients">
            <p>From:</p>
            <select name="client">
                <cfloop query="client_menu">
                    <option value="#client_menu.id#">#client_menu.name#</option>
                </cfloop>
            </select>
            <input class="btn btn-success" type="Submit" name="submit_to_graph" value="Submit" id="submit_to_graph">
        </form>
    </div>

And here is my jQuery function I have so far:

<script type="text/javascript">
$(function() {
    $("#graph_select").change(function() {
        if($("#pilot_form").is(":selected")) {
            $("#pilot_graph_form").css({"display":"block"});
        }
        else {
            $("#pilot_graph_form").css({"display":"none"});
        }
        if($("#client_form").is(":selected")) {
            $("#client_graph_form").css({"display":"block"});
        }
        else {
            $("#client_graph_form").css({"display":"none"});
        }
    });
});
</script>

Answer 1

First of all, you should change "id" on your "option" to "value".

Then you can use this:

$(function () {
  $("#graph_select").change(function() {
    var val = $(this).val();
    if(val === "pilot_form") {
        $("#pilot_graph_form").show();
        $("#client_graph_form").hide();
    }
    else if(val === "client_form") {
        $("#client_graph_form").show();
        $("#pilot_graph_form").hide();
    }
  });
});

Answer 2

$(function() {
  $("#graph_select").change(function() {
    if ($("#pilot_form").is(":selected")) {
      $("#pilot_graph_form").show();
      $("#client_graph_form").hide();
    } else {
      $("#pilot_graph_form").hide();
      $("#client_graph_form").show();
    }
  }).trigger('change');
});

DEMO