Aline is written in standard form ax + by = 0, where a and b are not
both zero. find the coordinates of the point that must lie on this line, no
matter what the choice of a and b.

A point that must lie on this line is the origin (0,0)

Step-by-step explanation:

we know that

The equation of the line in standard form is equal to

where

A is a positive integer

B and C are integer

In this problem

C=0

so

That means, that the line represent a proportional relationship between the variables x and y

Remember that in a proportional relationship the line passes through the origin

therefore

A point that must lie on this line is the origin (0,0)