Young's Modulus in the form y = mx + c Watch
Ambiguous I know
Anyway, since stress is on the y-axis and strain is on the x-axis (hopefully) then change in stress/change in strain is equal to the Young's modulus and also the gradient. That's your "m".
Your +c would be the value of stress when strain = 0. Ideally the line should pass through the origin.
So, for the bit of the graph that's linear, stress = Young modulus * strain + c (hopefully it goes straight through the origin).
Young's Modulus, E, = stress/strain
E = FL/(A delta L)
because F = T = W where W = Mg (use capital M for mass here so not to confuse little m for gradient)
So, substituting for F
E = (Mg L) / (A delta L)
Now re-arrange to put into y=mx+c
delta L = (L / AE) x Mg you would not normally need to put the +0 for +c here denoting the intercept is at the origin.
Interestingly as the gradient, m, = (L / AE) this can be re-arranged for an approximation of E because E = L / mA. This is very useful if you are to complete the Young's Modulus Required Practical in AS Physics...
Hope this helps.