Answer:
[tex]y-6=-\frac3{13}(x-5)[/tex]
Step-by-step explanation:
Get the slope of the line between the two points. As usual, [tex]m= \frac{\Delta y}{\Delta x}= \frac{8-(-18)}{4-(-2)}=\frac{8+18}{4+2}=\frac{26}{6}=\frac{13}3[/tex]
You want the perpendicular to it, so take it's inverse and change its sign:
[tex]m_p=-\frac3{13}[/tex]
At this point, it's just using the point-slope form, and you're done - unless you're required to provide the line in a specific way, which usually means just crunching numbers and rewriting the equation
[tex]y-y_0=m_p(x-x_0)\\y-6=-\frac3{13}(x-5)[/tex]
