1. **State the problem:** Solve the linear equation $y - 3x - 1 = 0$ for $y$. 2. **Rewrite the equation:** The equation is given as $y - 3x - 1 = 0$. 3. **Isolate $y$:** Add $3x + 1$ to both sides to isolate $y$: $$y - 3x - 1 + 3x + 1 = 0 + 3x + 1$$ This simplifies to: $$y = 3x + 1$$ 4. **Interpretation:** The equation $y = 3x + 1$ is the slope-intercept form of a line, where the slope is 3 and the y-intercept is 1. **Final answer:** $$y = 3x + 1$$