Question
y = –4x + 9
Hint: The standard form of a linear equation isAx + By = C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Hint: The standard form of a linear equation isAx + By = C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Answers
GPT-4o mini
To convert the given equation \( y = -4x + 9 \) into standard form \( Ax + By = C \) where \( A \), \( B \), and \( C \) are integers, follow these steps:
1. Start with the original equation:
\[
y = -4x + 9
\]
2. Rearrange the equation to get the terms involving \( x \) and \( y \) on the same side:
\[
4x + y = 9
\]
3. Now identify the coefficients:
- \( A = 4 \)
- \( B = 1 \)
- \( C = 9 \)
4. Check if the GCF of \( A \), \( B \), and \( C \) is 1. The GCF of \( 4, 1, \) and \( 9 \) is 1, so we are all set.
Thus, the standard form of the equation is:
\[
4x + y = 9
\]
1. Start with the original equation:
\[
y = -4x + 9
\]
2. Rearrange the equation to get the terms involving \( x \) and \( y \) on the same side:
\[
4x + y = 9
\]
3. Now identify the coefficients:
- \( A = 4 \)
- \( B = 1 \)
- \( C = 9 \)
4. Check if the GCF of \( A \), \( B \), and \( C \) is 1. The GCF of \( 4, 1, \) and \( 9 \) is 1, so we are all set.
Thus, the standard form of the equation is:
\[
4x + y = 9
\]