Question

Write an equation for a line

Answer 1

$k: y = mx + b$
$l: y = nx + c$
$l\ \perp\ k\ \iff\ m\cdot n = -1$
We have:
$k:\ f(x)=5x-8\\\\l:\ g(x)=mx+b\\\\l\ \perp\ k\iff 5m=-1\ \ \ |:5\to m=-\dfrac{1}{5}$

therefore
$l:\ y=-\dfrac{1}{5}x+b$
The line passing through the point (5; 10).
Substitute the values of the coordinates of the point
$(5;\ 10)\to x=5;\ y=10\\\\10=-\dfrac{1}{5}\cdot5+b\\\\10=-1+b\ \ \ \ |+1\\\\b=11$
$Answer:\ \boxed{y=-\dfrac{1}{5}x+11}$