6. Rearrange each of the following formulae to make the letter in the brackets the subject. \( \begin{array}{l}\text { (a) } X=\frac{2}{3} Y+15\end{array} \quad[Y] \)

To rearrange the formula \( X = \frac{2}{3} Y + 15 \) to make \( Y \) the subject, follow these steps: 1. **Subtract 15 from both sides:** \[ X - 15 = \frac{2}{3} Y \] 2. **Multiply both sides by \( \frac{3}{2} \) to isolate \( Y \):** \[ Y = \frac{3}{2} (X - 15) \] 3. **Simplify the expression:** \[ Y = \frac{3}{2} X - \frac{45}{2} \] **Final Answer:** \[ Y = \frac{3}{2} X - \frac{45}{2} \]