How do you show a line is a tangent to a curve?
You do this by picking a point on the curve so that you have its (x,y) coordinates.
You then find the derivative of the curve. The derivative is the expression that represents the slope of the curve. Substitute in the x value from the (x,y) coordinate obtained in the first step. This will then give you a numeric value for the slope of the tangent line at that point.
Next use either the point slope formula or the y-intercept formula to derive the equation of the tangent line.
Please see the video examples.