Question

standard form
write the standard form of the equation of each line.

1. $4x = 7 - 3y$
2. $10 + 2y = 9x$
3. $-8 = -x + 2y$
4. $-2y = x$

Explanation:

Problem 1: \( 4x = 7 - 3y \)

Step 1: Recall standard form

The standard form of a linear equation is \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \geq 0 \).

Step 2: Rearrange the given equation

We have \( 4x = 7 - 3y \). Add \( 3y \) to both sides to get \( 4x + 3y = 7 \).

Step 1: Recall standard form

The standard form of a linear equation is \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \geq 0 \).

Step 2: Rearrange the given equation

We have \( 10 + 2y = 9x \). Subtract \( 9x \) from both sides and subtract \( 10 \) from both sides to get \( -9x + 2y = -10 \). Multiply both sides by \( -1 \) to make \( A \geq 0 \), so \( 9x - 2y = 10 \).

Step 1: Recall standard form

The standard form of a linear equation is \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \geq 0 \).

Step 2: Rearrange the given equation

We have \( -8 = -x + 2y \). Add \( x \) to both sides to get \( x - 2y = -8 \).

Answer:

\( 4x + 3y = 7 \)

Problem 2: \( 10 + 2y = 9x \)