How to NOT have the markers on a regression line

I am trying to make a scatter plot with points and a fitted regression line (lm in my case). The example in the beginning of R figure reference does almost the trick, but there is a problem that I could not solve. In the plot there is the fitted line, but it contains markers for all the points (the x-values projected to the line). You cannot even see a glimpse of the actual line, because the markers completely hide it. The mode is ‘lines’, but it seems that it behaves like mode=‘lines+markers’.

As you can see in the picture, the fitted line is very thick, because all the markers are drawn on it. The hover shows a marker on the line and it is one of the datapoints projected on top of the line.

How can I get just the line, not the markers?