To rewrite the given equation [tex]\( y - 4 = -2(x + 7) \)[/tex] in standard form, let's follow these steps:
1. Start with the given equation:
[tex]\[
y - 4 = -2(x + 7)
\][/tex]
2. Distribute the [tex]\(-2\)[/tex] on the right side of the equation:
[tex]\[
y - 4 = -2x - 14
\][/tex]
3. Add [tex]\(4\)[/tex] to both sides to isolate the [tex]\(y\)[/tex] term on the left:
[tex]\[
y - 4 + 4 = -2x - 14 + 4
\][/tex]
Simplifying this, we get:
[tex]\[
y = -2x - 10
\][/tex]
4. To convert this to standard form [tex]\(Ax + By = C\)[/tex], where [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are integers and [tex]\(A\)[/tex] is positive, we rearrange the equation:
[tex]\[
2x + y = -10
\][/tex]
Thus, the equation in standard form is [tex]\(2x + y = -10\)[/tex], hence the correct answer is:
4. [tex]\(2x + y = -10\)[/tex]
