Find the slope and the equation of the line passing through the points:

The slope of the equation can be calculated using

$\mathrm{m}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{-4-1}{2-(-1)}=\frac{-5}{3}$

$\mathrm{~m}=-\frac{5}{3}$

Now using two point form of the equation of a line

$\mathrm{y}-\mathrm{y}_{1}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\left(\mathrm{x}-\mathrm{x}_{1}\right)$ where $\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}=$ slope of line

$y-1=\frac{-5}{3}(x-(-1)) \Rightarrow 3(y-1)=-5(x+1)$

$3 y-3+5 x+5=0$

$5 x+3 y+2=0$

So, required equation of line is $5 x-8 y-31=0$.