what actually a logistic regression fits

Dear all:
    I did the following because I was not sure what a logistic regression
fits ."small.glm" is a glm fit , setting the family to be binomial.

fitted(small.glm)->p
log(p/(1-p))->left   
for(i in 1:length(coef(small.glm))){

+  coef(small.glm)[i]*model.matrix(small.glm)[,i]->res[,i]
+ }

apply(res,1,sum)->right
plot(left,right)  #I got a straight line whose slope was about 1

Therefore ,I am almost sure that what a logistic regression fits is
log(p/(1-p))~b0+b1*x.
Is that right? 
Regards,

-----
Best regards,
Bin Yue

*************
student for a Master program in South Botanical Garden , CAS

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