GIMP :: Change All Pixels Of One Value To A Different Value

I have a diagram scanned in one pixel mode (b&w). I want to change the line color from black to blue.

I tried this:

In the toolbox I altered the foreground color to blue. In the 'Select' menu I used the 'By color' option. I made sure the settings in the toolbox for 'Select by color' were set at default, then I clicked on a black pixel in the image. The black lines in the image became outlined with a dotted line. I then used the 'Fill with FG color' option from the edit menu. The sample color to the left of the menu item was blue. The image briefly 'repainted'. I removed the selection using 'Select' 'None' but the image lines remain black.