Either do a separate regression analysis for all geographic sections using rainfall and amount of vegetation as independent and dependent variables; or build one (multilevel) regression model forcing 2-way interaction terms between rainfall and a series of dummy variables for each region (minus a reference region). In the latter case, the effect of rainfall on vegetation per region would then be expressed as the coefficient for rainfall plus the coefficient of the interaction term of the appropriate region's dummy (in the reference region the rainfall coefficient alone is the effect).
Note that both these options would require multiple measures per region. If this is indeed available, then within the regions there is bound to be some auto-correlation. This could also be modeled using a multilevel/random effects model. Although it will not give you clear estimates on the effect of rainfall for each section, adding a 'random slope' to such a model will estimate a mean effect of rainfall on vegetation (the coefficient) and a standard deviation across regions for the effect of rainfall on vegetation, taking into account auto-correlation.