Google-sheets – How to use Google Spreadsheets to chart completed tasks using time series graph

Maybe this has been fixed in New Google Sheets because it works for me (indeed, it is VERY simple):

Select A1:B3, Insert, Chart..., click Line chart, Insert.

Seems happy to work with DMY format and, as it happens, text for dates (since happening to be 4 months apart the x-axis spacing to be equal is about correct anyway).

I don't think this is possible, since there is no onClick-trigger.
There are alternatives, though, using scripts. I've built two different ways.

Dropdown
Use a dropdown where you select the number of the column to choose from.

A button (drawing)
Click on a drawing with a script assigned to it updating the scripts source range.

See example of both here. The "Click me" drawing has the script updateChart-function assigned to it.

Since you have your chart-ranges on the x-axis I've used Mogsdad's method to Switch rows / columns programmatically. The method requires the 2D Arrays Library, read here how to install it. It also requires you to have a sheet named Scratch, you can hide it, though.

Here's the code used:

function onEdit(e) {
  var sheet = SpreadsheetApp.getActiveSheet();
  if (sheet.getName() == "Chart Sheet"){
    //var sourceRange = e.source.getActiveRange();
    var sourceRow = 1;//sourceRange.getRow();
    var sourceColumn = 1;//sourceRange.getColumn();
    var sourceRange = sheet.getRange(sourceRow, sourceColumn)
    var sourceValue = sourceRange.getValue();
    var lastCol = sheet.getLastColumn();
    var newRange = sheet.getRange(sourceValue + 1, 2, 1, lastCol);


    if(sourceRow == 1 && sourceColumn == 1){ //Address to cell with dropdown, placed in corner not to interfere with getLastColumn

      var srcData = sheet.getRange(sourceValue + 1, 2, 1, lastCol).getValues();

      // Transpose the table (using 2D Array Library)
      var scratchData = ArrayLib.transpose(srcData);

      var numRows = scratchData.length;
      var numCols = scratchData[0].length; // assume all rows are same width

      // Write scratch values to scratch sheet.
      var scratchSheet = SpreadsheetApp.getActiveSpreadsheet().getSheetByName("Scratch");
      scratchSheet.getRange(1, 1, numRows, numCols).setValues( scratchData );
      SpreadsheetApp.flush();



      var chart = sheet.getCharts()[0];
        var oldRange = chart.getRanges()[0];
        chart = chart.modify()
        .removeRange(oldRange)
        .addRange(scratchSheet.getDataRange())
        .build();
        sheet.updateChart(chart);
      }
    }
}

function updateChart(){
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getActiveSheet();
  var lastCol = sheet.getLastColumn();
  var row = sheet.getActiveRange().getRow();
  var newRange = sheet.getRange(row, 1, 1, 3);

  var srcData = sheet.getRange(row, 2, 1, lastCol).getValues();

  // Transpose the table (using 2D Array Library)
  var scratchData = ArrayLib.transpose(srcData);

  var numRows = scratchData.length;
  var numCols = scratchData[0].length; // assume all rows are same width

  // Write scratch values to scratch sheet.
  var scratchSheet = SpreadsheetApp.getActiveSpreadsheet().getSheetByName("Scratch");
  scratchSheet.getRange(1, 1, numRows, numCols).setValues( scratchData );
  SpreadsheetApp.flush();

  var chart = sheet.getCharts()[0];
  var oldRange = chart.getRanges()[0];
  chart = chart.modify()
  .removeRange(oldRange)
  .addRange(scratchSheet.getDataRange())
  .build();
  sheet.updateChart(chart);
  sheet.getRange(1, 1).setValue(row - 1); //This row is only necessary if both methods are used
}

I hope this helps, ask me if you have any questions!