# Equation of a Line

I have following stuff

$(x_1, y_1) = (3, 36)$ with $m = -10$, $c=66$ (got it from $x_2$, $y_2$)

$(x_2, y_2) = (3.5, 31)$ with $m = -8$, $c=59$ (got it from $x_3$, $y_3$)

Now I have another coordinate value that is $(x', y') = (x', 33.8)$

So let me know How can I get $x'$ value ? (I need to find-out shortest path then calculate it)
EDIT:: I have list of $x, y$ and corresponding $m$ and $c$ values. Now I get another coordinate points without $x$. So how can I find out $x$? I can easily find out $y=mx+c$ or by using $m = \dfrac{y_2-y_1}{x_2-x_1}$ formula. But How can I identify which m's value should I use. Like in above values. How can get x' value by using $-10$ or by $-8$. Or anything else way.