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

Question

y = C−Ax

y = B(C − Ax)

y=C− Ax/B

y=C/B−Ax/B

Answer 1

To solve for \( y \) in the equation \( Ax + By = C \), follow these steps:

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

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

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

4. This can also be rewritten as: \[ y = \frac{C}{B} - \frac{Ax}{B} \]

So, the correct expression for \( y \) is: \[ y = \frac{C - Ax}{B} \] or equivalently, \[ y = \frac{C}{B} - \frac{A}{B}x \]

Thus, all steps you provided lead to the correct form of \( y \):

• \( y = \frac{C - Ax}{B} \)
• \( y = \frac{C}{B} - \frac{Ax}{B} \)

Both forms are valid, but the simplest direct solution is: \[ y = \frac{C - Ax}{B} \]