Sure! Let's start by solving the equation [tex]\( y = \frac{1}{3}(x + 2) \)[/tex] step by step to find [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
1. Start with the given equation:
[tex]\[
y = \frac{1}{3}(x + 2)
\][/tex]
2. Multiply both sides by 3 to eliminate the fraction:
[tex]\[
3y = x + 2
\][/tex]
3. Solve for [tex]\( x \)[/tex] by isolating it on one side of the equation:
[tex]\[
x = 3y - 2
\][/tex]
Now, let's compare [tex]\( x = 3y - 2 \)[/tex] with the given options to find which is equivalent:
1. Option 1: [tex]\( x = y - \frac{11}{3} \)[/tex]
2. Option 2: [tex]\( x = y + \frac{7}{3} \)[/tex]
3. Option 3: [tex]\( x = 3 \left( y - \frac{2}{3} \)[/tex] \)
Simplify this option:
[tex]\[
x = 3 \left( y - \frac{2}{3} \right) = 3y - 2
\][/tex]
This matches our calculated equation.
4. Option 4: [tex]\( x = 3 \left( y + \frac{2}{3} \)[/tex]
Let's box the correct option to make it clear:
[tex]\[
\boxed{x = 3\left(y - \frac{2}{3}\right)}
\][/tex]
The correct solution is:
[tex]\( x = 3\left(y - \frac{2}{3}\right) \)[/tex]
