In order to find the equation of this line, let's use the slope-intercept form of the linear equation and the given points:
[tex]\begin{gathered} y=mx+b \\ \\ (2,3)\colon \\ 3=2m+b \\ \\ (-3,4)\colon \\ 4=-3m+b\to b=4+3m \\ \\ 3=2m+(4+3m)_{}_{} \\ 3=5m+4 \\ 5m=3-4 \\ 5m=-1 \\ m=-\frac{1}{5} \\ \\ b=4+3(-\frac{1}{5}) \\ b=4-\frac{3}{5}=\frac{20}{5}-\frac{3}{5}=\frac{17}{5} \\ \\ y=-\frac{1}{5}x+\frac{17}{5} \end{gathered}[/tex]