In general, to provide your own formula you should use arguments x and y that will correspond to values you provided in ggplot() – in this case x will be interpreted as x.plot and y as y.plot. You can find more information about smoothing methods and formula via the help page of function stat_smooth() as it is the default stat used by geom_smooth().
ggplot(data,aes(x.plot, y.plot)) +
stat_summary(fun.data=mean_cl_normal) +
geom_smooth(method='lm', formula= y~x)
If you are using the same x and y values that you supplied in the ggplot() call and need to plot the linear regression line then you don’t need to use the formula inside geom_smooth(), just supply the method="lm".
ggplot(data,aes(x.plot, y.plot)) +
stat_summary(fun.data= mean_cl_normal) +
geom_smooth(method='lm')