The reason for looking at the assumption of linearity and homoscedasticity together is that we can check both with a single graph. Both assumptions relate to the errors (a.k.a. residuals) in the model and we can plot the values of these residuals against the corresponding values of the outcome predicted by our model in a scatterplot. The resulting plot shows whether there is a systematic relationship between what comes out of the model (the predicted values) and the errors in the model.
