$5.$ Consider the differential equation $\backslash (\backslash$frac$\{$d y$\}\{$d x$\}=$y$+$x y $\backslash ).$

a$)$ Sketch a slope field for the points on a window of $\backslash ([-3,3]\backslash )$ by $\backslash ([-3,3]\backslash ).(3$ points$)$

b$)$ Describe where horizontal tangent lines will occur and justify your conclusion. $(3$ points$)$

c$)$ Describe when the slopes will be positive and explain$/$justify algebraically $($not just from the observations of your slope field$).(3$ points$)$

d$)$ Describe where, or if$,$ any vertical tangent lines occur and justify your answer. $(1$ point$)$