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The purpose of this paper is to examine the condition for a Finsler space with a generalized α,β-metric to be projectively flat. In addition, we establish that the Finsler space with generalized α,β-metric is a flat-parallel Minkowski space and derive the condition under which the β-change for the aforementioned metric is projective. We also explored the projective nature of β-change for various significant Finsler metrics derived from the generalized α,β-metric.