How to randomly generate points in a line?

Question

For example,how to randomly generate 100 points in line L:y=x,and x~N(0,1).

Edit:I mean,for point p(x,y),x=t,y=t,t is random variable，and t~N(0,1).Randomly generate 100 points like it.

Answer 1

Maybe

{#, #} & /@ RandomVariate[NormalDistribution[0, 1], 100]
% // Point // Graphics

Answer 2

Clear["Global`*"]

line = Line[{{-3, -3}, {3, 3}}];

SeedRandom[1234];

For uniformly distributed points on the line

ptsU = RandomPoint[line, 1000];

For normally distributed points on the line

ptsN = RandomVariate[TruncatedDistribution[{-3, 3},
     NormalDistribution[]], 1000];

Histogram[{ptsN, ptsU[[All, 1]]}, Automatic, "PDF"]

Answer 3

Or

Graphics[
 Table[Point[{tmp = RandomVariate[NormalDistribution[0, 1]], 
    tmp}], {100}]]