The equation of the line passing through the point  $(2,–3)$ and parallel to the line joining the points  $(1,2)(–1,5)$ is

Let $(x_1,y_1)=(1,2)$

Let  $(x_2,y_2)=(-1,5)$

Equation of two points is:  $\frac{y-y_1}{y_1-y_2}=\frac{x-x_1}{x_1-x_2}$

$\frac{y-2}{2-5}=\frac{x-1}{1+1}$

$2y-4=-3x+3$

$3x+2y-7=0$

Equation of the line parallel to  $3x+2y-7=0$ is

$3x+2y+k=0$

But this line passing through  $(2,-3)$

$3\left(2\right)+2(-3)+k=0$

$k=0$

$\therefore$  equation of line is  $3x+2y=0$