# What is the equation of the line that passes through the origin and is perpendicular to the line that passes through the following points: (9,4),(3,8) ?

Feb 26, 2016

see below

#### Explanation:

The slope of the the line passing through (9,4) and (3,8) = $\frac{4 - 8}{9 - 3}$
$- \frac{2}{3}$
so any line perpendicular to the line passing through (9,4) and (3,8) will have slope (m) = $\frac{3}{2}$
Hence we are to find out the equation of the line passing through (0,0) and having slope = $\frac{3}{2}$
the required equation is
$\left(y - 0\right) = \frac{3}{2} \left(x - 0\right)$
i.e$.2 y - 3 x = 0$