The assumption of Linearity in linear regression is crucial as it ensures a straight-line relationship between the independent and dependent variables, implying that changes in the independent variable lead to proportional changes in the dependent variable. This is foundational for the model's accuracy. Other assumptions like Independence (observations are independent), Normality (errors are normally distributed), and Homoscedasticity (constant variance of errors) are important but do not directly address the proportionality of change between variables.