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A lightweight JavaScript class for drawing line graphs in a canvas element, that doesn't do any DOM manipulations. - linea/Graph.js ...
The best plan I've come up with so far as regards a graph being shown whilst it is running is re-doing it all in javascript ('cos I know I can do that).
A quadratic function can be drawn as a parabola on a graph. Find out how to plot the graph in this Bitesize KS3 maths video.
A linear equation is drawn as a straight line on a set of axes. To draw the graph we need coordinates. We generate these coordinates by substituting values into the linear equation.
JavaScript playground for drawing planar graphs (eg. fullerenes) in browser, or as eg. PostScript file with command line tool rjs (run nodejs script) and "JavaScript with C includes" script.