Question:
Show that the line through the points (5, 6) and (2, 3) is parallel to the line through the points (9, -2) and (6, -5)
Solution:
We know that for two lines to be parallel, their slope must be the same.
Given points are $A(5,6), B(2,3)$ and $C(9,-2), D(6,-5)$
slope $=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\right)$
$\Rightarrow\left(\frac{3-6}{2-5}\right)=\left(\frac{-5+2}{6-9}\right)$
$\Rightarrow\left(\frac{-3}{-3}\right)=\left(\frac{-3}{-3}\right) \Rightarrow 1=1$
Hence proved.