Question 990623
You have an unknown line with general points,  (x, -2x-3).  This point is same distance from point (-1,6) as from point  (-2,9).



Distance Formula will give the equation to express that reworded description.
{{{sqrt((x-(-1))^2+(-2x-3-(6))^2)=sqrt((x-(-2))^2+(-2x-3-9)^2)}}}



Analyze that for it to all make sense.  You can then continue with the algebraic steps to simplify the equation and solve for x.