Question

Write an equation for a line

g(x)
perpendicular to
f(x) = 5x − 8
and passing through the point
(5, 10)

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=-(1)/(5)`

therefore

`l:\ y=-(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=-(1)/(5)\cdot5+b\\\\10=-1+b\ \ \ \ |+1\\\\b=11`

`Answer:\ \boxed{y=-(1)/(5)x+11}`