Oh, dear. is a parabola, NOT any line at all! What you mean is that the derivative of so gives the slope of the tangent line.
Given that, at x= a, the derivative is and the value is . That means that the equation of the tangent line, at x= a, is . Saying that line goes through (0, -8) mean that x= 0, y= -8 makes that a true equation: solve .