Finding the slope of a tangent line

[Teh]

View attachment 6115
My professor shown us in class how to find the slope but I still don't understand

 

[HallsofIvy]

Find which slope? Surely your professor, when showing how to find slope explained that only straight lines have a single slope. Other curves, including "broken line curves" like this, have different slopes at different points. Here there are three different straight lines, one from (-5, 5) to (-2, 2), another from (-2, 2) to (0, 4), and the third from (0, 4) to (4, 2). What is the slope of each of those?