The create option would be the proper place to set an initial value
$(function () {
$('#slider-container').slider({
range: true,
min: 299,
max: 1099,
values: [299, 1099],
create: function() {
$("#amount").val("$299 - $1099");
},
slide: function (event, ui) {
$("#amount").val("$" + ui.values[0] + " - $" + ui.values[1]);
var mi = ui.values[0];
var mx = ui.values[1];
filterSystem(mi, mx);
}
})
});