1. **State the problem:** Solve the linear equation $2x + 3y = 30$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This involves moving terms and dividing by the coefficient of $y$. 3. **Isolate $y$:** $$2x + 3y = 30$$ Subtract $2x$ from both sides: $$3y = 30 - 2x$$ 4. **Divide both sides by 3:** $$y = \frac{30 - 2x}{3}$$ 5. **Simplify the expression:** $$y = 10 - \frac{2}{3}x$$ 6. **Interpretation:** This is the equation of a line in slope-intercept form $y = mx + b$, where the slope $m = -\frac{2}{3}$ and the y-intercept $b = 10$. This means for every increase of 3 in $x$, $y$ decreases by 2. **Final answer:** $$y = 10 - \frac{2}{3}x$$