Fit to the bounds of a LineString

Get the bounds of a LineString by passing its first coordinates to LngLatBounds and chaining extend to include the last coordinates.
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>Fit to the bounds of a LineString</title>
<meta name="viewport" content="initial-scale=1,maximum-scale=1,user-scalable=no" />
<script src="https://api.mapbox.com/mapbox-gl-js/v1.10.1/mapbox-gl.js"></script>
<link href="https://api.mapbox.com/mapbox-gl-js/v1.10.1/mapbox-gl.css" rel="stylesheet" />
<style>
	body { margin: 0; padding: 0; }
	#map { position: absolute; top: 0; bottom: 0; width: 100%; }
</style>
</head>
<body>
<style>
.btn-control {
font: bold 12px/20px 'Helvetica Neue', Arial, Helvetica, sans-serif;
background-color: #3386c0;
color: #fff;
position: absolute;
top: 20px;
left: 50%;
z-index: 1;
border: none;
width: 200px;
margin-left: -100px;
display: block;
cursor: pointer;
padding: 10px 20px;
border-radius: 3px;
}
 
.btn-control:hover {
background-color: #4ea0da;
}
</style>
<div id="map"></div>
<button id="zoomto" class="btn-control">Zoom to bounds</button>
 
<script>
	// TO MAKE THE MAP APPEAR YOU MUST
	// ADD YOUR ACCESS TOKEN FROM
	// https://account.mapbox.com
	mapboxgl.accessToken = '<your access token here>';
// A GeoJSON object with a LineString route from the White House to Capitol Hill
var geojson = {
'type': 'FeatureCollection',
'features': [
{
'type': 'Feature',
'geometry': {
'type': 'LineString',
'properties': {},
'coordinates': [
[-77.0366048812866, 38.89873175227713],
[-77.03364372253417, 38.89876515143842],
[-77.03364372253417, 38.89549195896866],
[-77.02982425689697, 38.89549195896866],
[-77.02400922775269, 38.89387200688839],
[-77.01519012451172, 38.891416957534204],
[-77.01521158218382, 38.892068305429156],
[-77.00813055038452, 38.892051604275686],
[-77.00832366943358, 38.89143365883688],
[-77.00818419456482, 38.89082405874451],
[-77.00815200805664, 38.88989712255097]
]
}
}
]
};
 
var map = new mapboxgl.Map({
container: 'map',
style: 'mapbox://styles/mapbox/light-v10',
center: [-77.0214, 38.897],
zoom: 12
});
 
map.on('load', function() {
map.addSource('LineString', {
'type': 'geojson',
'data': geojson
});
map.addLayer({
'id': 'LineString',
'type': 'line',
'source': 'LineString',
'layout': {
'line-join': 'round',
'line-cap': 'round'
},
'paint': {
'line-color': '#BF93E4',
'line-width': 5
}
});
 
document.getElementById('zoomto').addEventListener('click', function() {
// Geographic coordinates of the LineString
var coordinates = geojson.features[0].geometry.coordinates;
 
// Pass the first coordinates in the LineString to `lngLatBounds` &
// wrap each coordinate pair in `extend` to include them in the bounds
// result. A variation of this technique could be applied to zooming
// to the bounds of multiple Points or Polygon geomteries - it just
// requires wrapping all the coordinates with the extend method.
var bounds = coordinates.reduce(function(bounds, coord) {
return bounds.extend(coord);
}, new mapboxgl.LngLatBounds(coordinates[0], coordinates[0]));
 
map.fitBounds(bounds, {
padding: 20
});
});
});
</script>
 
</body>
</html>