What is the graph of the equation ax + by = c if at least one of the numbers a or b is not zero?

Let’s transform the expression:

a * x + b * y = c;

a * x – c = – b * y;

y = – (a * x – c) / b = c / b – x * a / b.

If a = 0, then such a function does not exist.

If at ≠ 0, then the function has a graph of a straight line.

If at the same time a = 0, then this straight line will be parallel to the X-axis and y, for all values of x, will take on the value of c / b.