A $100mm**100mm$ wood lumber was subjected to bending with a span of $1\mathrm{.}5m$ until failure by applying a load in the middle of its span. The load and the deflection in the middle of the span were recorded as shown in the table below.

$\backslash$table$[[$Load $($N$),$Deflection $($mm$)],[0,0],[431,3406],[867,5189],[1517,6744],[3247,8344],[6005,9235],[8443,9990],[10235,10470],[13149,11476],[15475,12276],[17748,13282],[19750,14082]]$

a$.$ Plot the load$-$deflection relationship.

b$.$ Plot the proportional limit on the graph.

c$.$ Calculate the modulus of rupture $($flexure strength$).$