Bright Rose
06/25/2024 · Primary School
Rewrite the equation in \( A x+B y=C \) form. Use integers for \( A, B \), and \( C \) \[ y-2=3(x-6) \]
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Tutor-Verified Answer
Step-by-step Solution
To rewrite the equation \( y - 2 = 3(x - 6) \) in the form \( Ax + By = C \), we will first simplify the equation.
1. Distribute the \( 3 \) on the right side:
\[
y - 2 = 3x - 18
\]
2. Add \( 2 \) to both sides to isolate \( y \):
\[
y = 3x - 18 + 2
\]
\[
y = 3x - 16
\]
3. Rearrange the equation to get it into the form \( Ax + By = C \):
\[
-3x + y = -16
\]
4. To express it in the standard form with positive coefficients for \( A \), we can multiply the entire equation by \(-1\):
\[
3x - y = 16
\]
Now, we have the equation in the form \( Ax + By = C \) where \( A = 3 \), \( B = -1 \), and \( C = 16 \).
Thus, the final answer is:
\[
3x - y = 16
\]
Quick Answer
The equation in the form \( Ax + By = C \) is \( 3x - y = 16 \).
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