How to make a linear model with a constant value in R?

I'm working on an unassessed homework problem from unpublished course notes of a statistics module from a second year university mathematics course.

I'm trying to plot a 2-parameter full linear model and a 1-parameter reduced linear model for the same data set. I can't figure out how to plot the 1-parameter model; all attempts so far have either given errors or a non-constant slope.

xs - c(0,1,2)
ys - c(0,1,1)
Data - data.frame(x = xs, y = ys)
mf - lm(y ~ x, data = Data) # model_full
mr - lm(y = mean(y), data = Data) # model_reduced; this is the bit I can't get to work
attach(Data)
plot(x, y, xlab=x, ylab=y)
abline(mf$coefficients[1], mf$coefficients[2])
abline(mr$coefficients[1], mr$coefficients[2])