How do you find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points: (-5, -10) and (0, 0)?

Apr 14, 2015

The slope of a straight line through $\left({x}_{1} , {y}_{1}\right) = \left(- 5 , - 10\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(0 , 0\right)$ is given by

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$= \frac{0 - \left(- 10\right)}{0 - \left(- 5\right)}$

$= 2$

All parallel straight lines share the same slope.
so the slope of a line parallel to a line through $\left(- 5 , - 10\right)$ and $\left(0 , 0\right)$ is $m = 2$

The slope of a line perpendicular to a line with slope $m$ is
$- \frac{1}{m}$
or, in this case,
$- \frac{1}{2}$