Question

Rewrite the following equation in standard form.

y = –7x − 8


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.

Answer 1

To rewrite the equation \( y = -7x - 8 \) in standard form \( Ax + By = C \), we can follow these steps:

1. Start with the original equation:
\[
y = -7x - 8
\]

2. Add \( 7x \) to both sides to get \( x \) and \( y \) on the same side:
\[
7x + y = -8
\]

3. Now we need to express the equation in standard form, ensuring that \( A \), \( B \), and \( C \) are integers and that their greatest common factor (GCF) is 1. The current equation is:
\[
7x + y = -8
\]

4. To work with a standard form where \( C \) is positive, we can multiply the entire equation by -1:
\[
-7x - y = 8
\]

5. To make \( A \) positive (as typically required), we'll multiply through by -1 again:
\[
7x + y = -8
\]

The equation is now in standard form. It is:

\[
7x + y = -8
\]

Thus, the final answer in standard form is:
\[
7x + y = -8
\]