Question 980177
"...Passing through" (h,k) and (u,v).


Slope-Intercept form:  {{{y=mx+b}}}
{{{b=y-mx}}}


Slope, {{{m=(v-k)/(u-h)}}}.


Substitute expressions.
{{{y=((v-k)/(u-h))x+(y-mx)}}}
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Pick either "given" point and substitute into slope-intercept form.
{{{y=((v-k)/(u-h))x+(-3-((v-k)/(u-h))*4)}}}
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You can try to simplify this symbolic form if you want.
{{{y=((v-k)/(u-h))x+(4(v-k)/(u-h)-3(u-h)/(u-h))}}}
{{{highlight(y=((v-k)/(u-h))x+(4v-4k-3u+3h)/(u-h))}}}


Your example uses {{{system(h=4,k=-3,u=3,v=-2)}}}.
You could substitute the values early and compute & simplify your way to the answer.