To convert the given equation [tex]\( y + 3 = 7(x - 2) \)[/tex] into standard form, follow these steps:
1. Simplify the right side of the equation: Distribute the 7 to both terms inside the parentheses.
[tex]\[
y + 3 = 7x - 14
\][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side to move towards standard form: We need to move all terms to one side of the equation so that the equation is in the form [tex]\( Ax + By = C \)[/tex]. Start by moving the [tex]\( y \)[/tex]-term and the constant term on the left to the other side.
[tex]\[
y + 3 - y = 7x - 14 - y
\][/tex]
Simplifying this, we get:
[tex]\[
3 = 7x - y - 14
\][/tex]
3. Bring all the terms to one side of the equation: To achieve the standard form [tex]\( Ax + By = C \)[/tex], we aim to move all terms to one side (either left or right).
[tex]\[
3 + 14 = 7x - y
\][/tex]
Simplifying this, we get:
[tex]\[
17 = 7x - y
\][/tex]
4. Write the equation in the form [tex]\( Ax + By = C \)[/tex]: This is already in the required format just by moving around terms:
[tex]\[
7x - y = 17
\][/tex]
So, the given equation [tex]\( y + 3 = 7(x - 2) \)[/tex] in standard form is:
[tex]\[
7x - y = 17
\][/tex]
Looking at the provided options:
(A) [tex]\( -7x + y = -5 \)[/tex]
(B) [tex]\( y = 7x - 17 \)[/tex]
(C) [tex]\( -7x + y = -17 \)[/tex]
(D) [tex]\( y = 7x - 5 \)[/tex]
The correct answer is none of the above, but the equation [tex]\( 7x - y = 17 \)[/tex].
