Question 885044
The strategy you chose appears a good one:  Find slope and use point-slope equation form.


m for slope.
{{{m=(3-(-1))/(2-(-1))=(3+1)/(2+1)}}}
{{{m=4/3}}}


Pick either point and fill into {{{y-v=m(x-u)}}} for whichever point (u,v) you want.  You picked (2,3).
Point-Slope Form:   {{{highlight_green(y-3=(4/3)(x-2))}}}.


Why did you not continue?  You want the equation in standard form.  
{{{y-v=m(x-u)}}}
{{{y-v=mx-mu}}}
{{{mx-mu=y-v}}}
{{{mx-y-mu=-v}}}
{{{mx-y=mu-v}}}, a generalization of standard form.  The number properties applied are assumed understood.
Notice the left member is an expression linear in x and y, and the right member expression is a constant.  The slope is a rational number and you may need to use multiplicative inverse property to make the equation in its simplest form.