To convert the equation [tex]\( y - 3 = 15(x - 8) \)[/tex] to standard form, let's follow these steps:
1. Start with the given equation:
[tex]\[
y - 3 = 15(x - 8)
\][/tex]
2. Distribute 15 on the right-hand side:
[tex]\[
y - 3 = 15x - 120
\][/tex]
3. Isolate [tex]\( y \)[/tex] by adding 3 to both sides:
[tex]\[
y = 15x - 120 + 3
\][/tex]
Simplifying this, we get:
[tex]\[
y = 15x - 117
\][/tex]
4. Move all terms to one side to convert to standard form [tex]\( Ax + By = C \)[/tex]:
[tex]\[
y - 15x = -117
\][/tex]
Rearrange this to get the [tex]\( Ax + By = C \)[/tex] form, which usually has [tex]\( x \)[/tex] terms first:
[tex]\[
15x - y = 117
\][/tex]
Looking at the options given:
1. [tex]\( -15x + y = -117 \)[/tex]
2. [tex]\( 15x - y = -117 \)[/tex]
3. [tex]\( 15x - y = -5 \)[/tex]
4. [tex]\( -15x + y = -5 \)[/tex]
The correct conversion of the given equation to standard form from the listed options is:
[tex]\[
15x - y = -117
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{2}
\][/tex]
