1) Let's firstly plug into the equation, the quantity of y=1
[tex]\begin{gathered} -xy-x=y+3 \\ -x-x=1+3 \\ -2x=4 \\ \frac{-2x}{-2}=\frac{4}{-2} \\ x=-2 \\ (-2,1) \end{gathered}[/tex]
Note that after we plugged into that we have a point (-2,1).
2) Now, let's take the first derivative from the original equation. In this case, we need to take an implicit differentiation as you can see it below:
[tex]\begin{gathered} \frac{d}{dx}\lbrack-xy-x\rbrack=\frac{d}{dx}\lbrack y+3\rbrack \\ -\frac{d}{dx}\lbrack xy\rbrack-\frac{d}{dx}\lbrack x\rbrack=\frac{d}{dx}\lbrack y\rbrack+\frac{d}{dx}\lbrack3\rbrack \\ -xy^{\prime}-y-1=y^{\prime} \\ y^{\prime}=-\frac{y+1}{x+1} \end{gathered}[/tex]
3) Let's now find the slope:
