As a tangent is a straight line it is described by an equation in the form \(y - b = m(x - a)\). You need both a point and the gradient to find its equation. You are usually given the point - it's ...

Find \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...

An example of this can be seen below. Once the tangent is found you can use it to find the gradient of the graph by using the following formula: \(\text{Gradient to the curve =}~\frac {y_2-y_1} ...