Final answer:
The standard form of the equation y = 3/7x - 1 is 3x - 7y = 7, which corresponds to option (d). This is achieved by eliminating the fraction, moving all terms involving variables to one side, and ensuring the x-term's coefficient is positive.
Step-by-step explanation:
The original equation given is y = 3/7x - 1 To convert this equation to standard form (Ax + By = C), we can manipulate it by eliminating fractions and arranging terms so that x and y are on the same side of the equation. We will perform the following steps:
Multiply both sides of the equation by 7 to remove the fraction: 7y = 3x - 7.
Then, we rearrange the terms to get the x and y on the same side and the constant on the other side: -3x + 7y = -7.
As standard form usually has positive coefficients for the x-term, we can multiply the entire equation by -1 to make the coefficient of x positive: 3x - 7y = 7. This matches option (d).
The correct standard form of the equation is 3x - 7y = 7.