Find the derivative function of the equation, or the function from which you can calculate the slope of the graph at any given point. Your calculus class will discuss, in detail, how to find the derivatives of different kinds of functions. If the function is y=x2, for instance, the derivative will be dy/dx=2x.
Plug the point for which you want to find the tangent to the graph into the derivative formula. Let's say that you want the tangent at the point (2,4). At this point, dy/dx=4.
Plug the coordinates of the point in question, as well as the slope that you calculated in Step 2, into the slope-intercept equation, y=mx+b. You can directly plug in the x and y coordinates, and m is equal to the slope from Step 2. The object is to calculate the value of b. Plugging in yields 4=4*2+b. Thus, b=4-8=-4.
Write the final version of the tangent line. In our example, it is y=4x-4.