Drawing a slope field [R task]

We consider the differential equation

$\frac{\dd y}{\dd t}=1-2\,t\, y$

Create an R script that draws the slope field below for this differential equation by using only primitive graphical elements, such as segments to draw a segment (i.e., do not use the FlowField function).
Now write an R script that randomly draws 2,000 lineal elements in the region $0\le t\le 2, 0\le y\le 2,$ , as in the figure below. Just like iron filings make the field lines of a magnetic field visible, the random drawing of lineal elements gives an impression of solution curves of the differential equation.

Random line element field