There is example source code, how you can draw lines with OpenLayers. Draw one line: 
<!DOCTYPE html>
<html>
	<head>
		<title>DrawLine</title>
		<meta charset="utf-8" />
	</head>
	<body>
		<div id="map" style="top: 0; left: 0; bottom: 0; right: 0; position: fixed;"></div>
		<script src="http://www.openlayers.org/api/OpenLayers.js"></script>
		<script type="text/javascript">
			// Initialize
			var mapnik         = new OpenLayers.Layer.OSM(); // OpenStreetMap
			var fromProjection = new OpenLayers.Projection("EPSG:4326");   // Transform from WGS 1984
			var toProjection   = new OpenLayers.Projection("EPSG:900913"); // to Spherical Mercator Projection
			var lon			   = 24.9342;
			var lat			   = 60.2017;
			var position       = new OpenLayers.LonLat(lon, lat).transform( fromProjection, toProjection);
			var positiontwo    = new OpenLayers.LonLat(30.9342, 62.2017).transform( fromProjection, toProjection);
			var zoom           = 5; 
			var map = new OpenLayers.Map("map");
			map.addLayer(mapnik);
			// Add marker
			var markers = new OpenLayers.Layer.Markers( "Markers" );
			map.addLayer(markers);
			markers.addMarker(new OpenLayers.Marker(position));
			// Start and end point
			var start_point = new OpenLayers.Geometry.Point(lon, lat).transform( fromProjection, toProjection);
			var end_point = new OpenLayers.Geometry.Point(30.9342, 62.2017).transform( fromProjection, toProjection);
			// new vector graphic layer
			var vector = new OpenLayers.Layer.Vector();
			// Make line
			var line = new OpenLayers.Feature.Vector(new OpenLayers.Geometry.LineString([start_point, end_point]));
			// Add new feature to layer named by vector
			vector.addFeatures([line]);
			// Add vector layer to map
			map.addLayers([vector]);
			map.setCenter(position, zoom );
		</script>
	</body>
</html>
Draw multiple lines: 
<!DOCTYPE html>
<html>
	<head>
		<title>Draw MultiLines</title>
		<meta charset="utf-8" />
	</head>
	<body>
		<div id="map" style="top: 0; left: 0; bottom: 0; right: 0; position: fixed;"></div>
		<script src="http://www.openlayers.org/api/OpenLayers.js"></script>
		<script type="text/javascript">
			// Initialize
			var mapnik         = new OpenLayers.Layer.OSM(); // OpenStreetMap
			var fromProjection = new OpenLayers.Projection("EPSG:4326");   // Transform from WGS 1984
			var toProjection   = new OpenLayers.Projection("EPSG:900913"); // to Spherical Mercator Projection
			var lon			   = 24.9342;
			var lat			   = 60.2017;
			var position       = new OpenLayers.LonLat(lon, lat).transform( fromProjection, toProjection);
			var zoom           = 5; 
			var map = new OpenLayers.Map("map");
			map.addLayer(mapnik);
			// Add marker
			var markers = new OpenLayers.Layer.Markers( "Markers" );
			map.addLayer(markers);
			markers.addMarker(new OpenLayers.Marker(position));
			// Add Vector
			var vector = new OpenLayers.Layer.Vector();
			map.addLayers([vector]);
			// Start and end point
			var start_point = new OpenLayers.Geometry.Point(lon, lat).transform( fromProjection, toProjection);
			var end_point = new OpenLayers.Geometry.Point(30.9342, 62.2017).transform( fromProjection, toProjection);
			var line = new OpenLayers.Feature.Vector(new OpenLayers.Geometry.LineString([start_point, end_point]));
			vector.addFeatures([line]);
			// Line styles
			var style = {
				strokeColor: "#00FF00",
				strokeWidth: 5,
				strokeDashstyle: "dashdot",
			};
			// Add second end point
			var other_end_point = new OpenLayers.Geometry.Point(10.9342, 30.2017).transform( fromProjection, toProjection);
			// Add second line
			var geo = new OpenLayers.Geometry.LineString([start_point, other_end_point]);
			var secondLine = new OpenLayers.Feature.Vector(geo, null, style); // Add styles what we made earlie to Vector construct
			vector.addFeatures([secondLine]);
			map.setCenter(position, zoom );
		</script>
	</body>
</html>