Final answer:
The equation 3x - 5y = 30 can be transformed into the ax + by = 1 format by dividing each term by 30, resulting in (1/10)x - (1/6)y = 1. All lines with non-zero constant terms can be rewritten in this format.
Step-by-step explanation:
The equation 3x - 5y = 30 can be rewritten in the form ax + by = 1 by dividing every term by the same non-zero number. To find this number, divide 30, the constant term of the equation, by 1 since 1 is the desired constant term in the ax + by = 1 format.
Divide each term of the equation by 30 to get:
(3x/30) - (5y/30) = (30/30)
This simplifies to:
(1/10)x - (1/6)y = 1
To identify if there are lines whose equations cannot be rewritten in this form, we must recognize that any linear equation with a non-zero constant term can be rewritten in the ax + by = 1 form by dividing by the constant term. Thus, options A, B, C, and D can all be rewritten in this form, indicating that all lines with non-zero constant terms can be expressed in the ax + by = 1 format.