In[]:=
net=NetChain[​​{#,#}&[LinearLayer[1,"Input"1]//NetInitialize]​​]
Out[]=
NetChain
Input port:
vector (size: 1)
Output port:
vector (size: 1)

In[]:=
net=NetTrain[net,Table[{x}{.5-.1#+RandomReal[{-.01,.01}]&@x},{x,RandomReal[{-1,1},10]}]]
Out[]=
NetChain
Input port:
vector (size: 1)
Output port:
vector (size: 1)

Plot[net[x],{x,0,1}]
Out[]=
0.2
0.4
0.6
0.8
1.0
0.40
0.42
0.44
0.46
0.48
0.50
In[]:=
Table[​​Normal@NetExtract[NetExtract[net,layer],param],​​{layer,2},​​{param,{"Weights","Biases"}}​​]
Out[]=
{{{{-0.177519}},{0.389681}},{{{0.586321}},{0.27281}}}