Question

Write an equation of the line that is perpendicular to 5x + 20y = 10 and passes through the point (8, 3).

Answer 1

Given line ax+by=c and point (h, k), the perpendicular line through (h, k) can be written as
b(x-h) -a(y-k) = 0

In order for this to be in standard form, it must be rearranged somewhat, and any common factors removed.

We can start with
20(x-8) -5(y-3) = 0
4x -32 -y +3 = 0
4x -y = 29

The standard-form equation of the desired line through (8, 3) is
4x -y = 29