Remember that when you find a derivative, you're finding a formula that will give you the slope of the tangent line to any point on your function. So, when you plug in x = 0 into your derivative and get out y = 0 (good!), that value y = 0 is in SLOPE of the tangent line to your function at the point (0,0).
So now you now your tangent line has a slope of 0. Think about what kinds of lines have a slope of 0 - this should give you an idea of what your line is. Remember, lastly, that your line has to pass through your original point, (0,0). So what is the equation of a line with a slope of 0 that passes through (0,0)?