If you want to create an HTML element, use document.createElement function. SVG uses namespace, that's why you have to use document.createElementNS function.
var svg = document.getElementsByTagName('svg')[0]; //Get svg element
var newElement = document.createElementNS("http://www.w3.org/2000/svg", 'path'); //Create a path in SVG's namespace
newElement.setAttribute("d","M 0 0 L 10 10"); //Set path's data
newElement.style.stroke = "#000"; //Set stroke colour
newElement.style.strokeWidth = "5px"; //Set stroke width
svg.appendChild(newElement);