Parallel lines are a fixed distance apart and will never meet, no matter how long they are extended. Lines that are parallel have the same gradient. The graphs above, \(y = 2x + 1\) and \(y = 2x - 2\) ...

Now use the information you already have about finding the equation of a line and apply it to the dashed lines shown in these triangles. Remember, to find the equation of a line you need a point ...

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 ...