If the slope of the line joining the points A

If a line passing through $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \&\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ then slope of the line is given by

slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$

Given points are $A(x, 2)$ and $B(6,-8)$, and the slope is

$\frac{-5}{4}$

$\Rightarrow\left(\frac{-8-2}{6-x}\right)=\frac{-5}{4}$

$\Rightarrow\left(\frac{-10}{6-x}\right)=\frac{-5}{4} \Rightarrow-40=-30+5 x$

$\Rightarrow 5 x=-10$

$\Rightarrow x=-2$