1. **State the problem:** Find the equation of a line perpendicular to the line $y=\frac{3}{2}x - 1$ that passes through the point $(2, -3)$. 2. **Recall the slope of the given line:** The slope of the line $y=\frac{3}{2}x - 1$ is $m=\frac{3}{2}$. 3. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. $$m_{\perp} = -\frac{1}{m} = -\frac{1}{\frac{3}{2}} = -\frac{2}{3}$$ 4. **Use point-slope form to find the equation:** The point-slope form is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1) = (2, -3)$ and $m = -\frac{2}{3}$. $$y - (-3) = -\frac{2}{3}(x - 2)$$ $$y + 3 = -\frac{2}{3}x + \frac{4}{3}$$ 5. **Simplify to slope-intercept form:** $$y = -\frac{2}{3}x + \frac{4}{3} - 3$$ $$y = -\frac{2}{3}x + \frac{4}{3} - \frac{9}{3}$$ $$y = -\frac{2}{3}x - \frac{5}{3}$$ **Final answer:** $$y = -\frac{2}{3}x - \frac{5}{3}$$