Question
The standard form equation of a line is written as Ax + By = C.
Which equation is correctly solved for B?
Responses
A
B = -Ax + C
y
B = - Ax + C y
B
B = y
-Ax + C
B = y - Ax + C
C
B = Ax + C
y
B = Ax + C y
D
B = y
Ax + C
Which equation is correctly solved for B?
Responses
A
B = -Ax + C
y
B = - Ax + C y
B
B = y
-Ax + C
B = y - Ax + C
C
B = Ax + C
y
B = Ax + C y
D
B = y
Ax + C
Answers
Answered by
GPT-4o mini
To correctly solve for \( B \) in the standard form equation of a line \( Ax + By = C \), we need to isolate \( B \).
Starting from the equation:
\[
Ax + By = C
\]
we can subtract \( Ax \) from both sides:
\[
By = C - Ax
\]
Next, we divide every term by \( y \):
\[
B = \frac{C - Ax}{y}
\]
However, to express \( B \) clearly, we would write:
\[
B = \frac{C}{y} - \frac{Ax}{y}
\]
However, when comparing the given options, the correct manipulation to isolate \( B \) in a straightforward manner would more accurately adhere to the format seen in your provided options.
Therefore, the correct option, which matches the manipulations possibly overlooked, is:
**Option A:**
\[
B = -\frac{Ax}{y} + \frac{C}{y}
\]
**None of the options seem to follow a consistent valid transformation based on standard algebraic rules, but generally, isolating \( B \) in the way B = (C - Ax) / y captures the intention most directly. **
Unfortunately, all options appear to have presentation issues that stray from the common isolation of \( B \) in the equation. If you need further clarification or adjustment related to isolating variables or different forms, feel free to ask!
Starting from the equation:
\[
Ax + By = C
\]
we can subtract \( Ax \) from both sides:
\[
By = C - Ax
\]
Next, we divide every term by \( y \):
\[
B = \frac{C - Ax}{y}
\]
However, to express \( B \) clearly, we would write:
\[
B = \frac{C}{y} - \frac{Ax}{y}
\]
However, when comparing the given options, the correct manipulation to isolate \( B \) in a straightforward manner would more accurately adhere to the format seen in your provided options.
Therefore, the correct option, which matches the manipulations possibly overlooked, is:
**Option A:**
\[
B = -\frac{Ax}{y} + \frac{C}{y}
\]
**None of the options seem to follow a consistent valid transformation based on standard algebraic rules, but generally, isolating \( B \) in the way B = (C - Ax) / y captures the intention most directly. **
Unfortunately, all options appear to have presentation issues that stray from the common isolation of \( B \) in the equation. If you need further clarification or adjustment related to isolating variables or different forms, feel free to ask!