You take the straight-line portion of the graph before the elastic limit, find the slope. Young's modulus is that slope, because stress/strain in that linear region. In my lab manual, it's a neat dotted line from the origin... but when I watched Appa trying to straighten the bent rod of my broken ceiling fan last week, his strain was small but the stress on his face was very high. The graph for real things never starts at zero for people like us.
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