The equation of a line is given by Ax+ By = C. Solve for y

Question

y = C/B - Ax/B
y = C - Ax/B
y = C - Ax
y = B (C- Ax)

Answer 1

To solve the equation of a line given by \( Ax + By = C \) for \( y \), we can rearrange it. Here’s the step-by-step solution:

1. Start with the given equation: \[ Ax + By = C \]

2. Isolate the term containing \( y \) by subtracting \( Ax \) from both sides: \[ By = C - Ax \]

3. Next, divide both sides by \( B \) to solve for \( y \): \[ y = \frac{C - Ax}{B} \]

So, the correct form of \( y \) from the equation \( Ax + By = C \) is: \[ y = \frac{C - Ax}{B} \]

None of the answer options were formatted properly, but the correct isolation yields \( y = \frac{C}{B} - \frac{A}{B}x \). Thus, the first option you provided: \[ y = \frac{C}{B} - \frac{Ax}{B} \] is indeed the correctly derived form of \( y \).