We are given the equation [tex]\( 9x + 3y = 15 \)[/tex] and we need to solve for [tex]\( y \)[/tex].
First, we'll isolate [tex]\( y \)[/tex] on one side of the equation.
1. Start with the original equation:
[tex]\[
9x + 3y = 15
\][/tex]
2. Subtract [tex]\( 9x \)[/tex] from both sides to isolate the terms involving [tex]\( y \)[/tex] on one side:
[tex]\[
3y = 15 - 9x
\][/tex]
3. To solve for [tex]\( y \)[/tex], divide every term by 3:
[tex]\[
y = \frac{15 - 9x}{3}
\][/tex]
4. Simplify the right-hand side by dividing both terms in the numerator by 3:
[tex]\[
y = \frac{15}{3} - \frac{9x}{3}
\][/tex]
5. This simplifies to:
[tex]\[
y = 5 - 3x
\][/tex]
Thus, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is [tex]\( y = 5 - 3x \)[/tex].
Comparing this with the provided options:
A. [tex]\( y = -9x + 5 \)[/tex]
B. [tex]\( y = -3x + 5 \)[/tex]
C. [tex]\( y = -3x + 15 \)[/tex]
D. [tex]\( y = 9x + 15 \)[/tex]
The correct answer is:
B. [tex]\( y = -3x + 5 \)[/tex]
