Use https://sagecell.sagemath.org/ to run the SageMath code t,y = var('t y'); plot_slope_field(sin(y/2), (t,-5,5), (y,-5,5)) producing the direction field for the ODE \( {y'} = \sin\left(\frac{1}{2} \, {y}\right) \).

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 \(t= -3 \).

\[ {y'} = \sin\left(\frac{1}{2} \, {y}\right) \hspace{2em} y( -1 )= -2 \]