Use https://sagecell.sagemath.org/ to run the SageMath code t,y = var('t y'); plot_slope_field(y/15-t/3, (t,-5,5), (y,-5,5)) producing the direction field for the ODE \( {y'} = \frac{1}{15} \, {y} - \frac{1}{3} \, t \).

Let \(y_p\) be the solution to the following IVP. Explain how to use its direction field to approximate the value of \(y_p\) at \(t= 3 \).

\[ {y'} = \frac{1}{15} \, {y} - \frac{1}{3} \, t \hspace{2em} y( 1 )= 2 \]