線形回帰

最近Rの統計開発環境を使用してｌｍの関数を試しています。
I am confused about what exactly this function does. lm(y~x) supposedly computes a linear model in which y depends on x. Does this mean that a line through the data is computed. Outputs seem to consist of residuals and intercepts. Nowhere in the plots of an lm output is a line through a scatterplot indicated.
My guess about the meanings is as follows.
the equation for the correlation is:
y = mx + b, where b is the intercept.
Thus, I expect that, in the output of the lm function, the "intercept" is equivalent to b above and the "x" value is the coefficient equivalent to m. However, there is a "t" column which has values for both "intercept" and "x" rows. There is also a "Pr>t" column. I am uncertain about how these are interpreted. The residual values are y(actual)-y for each y, I assume. I have still yet to clarify the plots.
The "t value" and "Pr(>|t|)" columns seem to be related to testing the validity of the null hypothesis. I assume that the null hypothesis refers to the setting of either the slope or the intercept values to zero. However, I am not certain about how such a test is carried out or why a probability distribution is involved.