[R] How to interpret lm's coefficients?

[Matti Viljamaa]

I’m trying to understand how to interpret the return values, specifically “Coefficients:”, of R’s lm function. I’m using it with a dichotomic predictor (mom_hs).

lm(data$kid_score ~ data$mom_hs) returns 

Coefficients:
#   (Intercept)  data$mom_hs  
# 77.55        11.77

I read that the (Intercept) value is the “y-intercept” value b, i.e. the y value where the line intercept the y-axis.

The second value is the value of the term m (or “slope”) in the equation of a line y=mx+b.

However,

These two numbers also have the following interpretations:

b or (Intercept) value is the same as:
The mean of those data$kid_score that have data$mom_hs == 0.
Why is this a valid interpretation?

m or data$mom_hs value is the same as:
The difference of means between those data$kid_score that have data$mom_hs == 1
and those data$kid_score that have data$mom_hs == 0.
Why is this a valid interpretation?

Can someone explain?