homework and exercises - How does the equation $1/I = r/E +R/E$ relate to $y=mx+c$?

I have a graph of $1/$current against resistance, which is a straight line of positive gradient. I know that the gradient represents $1/V$ but I can't work out how the equation $1/I= r/E + R/E$ relates to $y=mx+c$. Could somebody please tell me what each part of $y=mx+c$ represents in relation to $1/I= r/E + R/E$?

Rearranged equation for Emf= IR + Ir