Question:
If the slope of the line joining the points $A(x, 2)$ and $B(6,-8)$ is $\frac{-5}{4}$, find the value of x.
Solution:
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
$\frac{-5}{4}$
$\Rightarrow\left(\frac{-8-2}{6-x}\right)=\frac{-5}{4}$
$\Rightarrow\left(\frac{-10}{6-x}\right)=\frac{-5}{4} \Rightarrow-40=-30+5 x$
$\Rightarrow 5 x=-10$
$\Rightarrow x=-2$