1. **State the problem:** Find the equation of the line passing through points $(2, -3)$ and $(4, 2)$ in standard form. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** $$m = \frac{2 - (-3)}{4 - 2} = \frac{2 + 3}{2} = \frac{5}{2}$$ 4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1)$$ Using point $(2, -3)$: $$y - (-3) = \frac{5}{2}(x - 2)$$ $$y + 3 = \frac{5}{2}x - 5$$ 5. **Simplify to slope-intercept form:** $$y = \frac{5}{2}x - 5 - 3$$ $$y = \frac{5}{2}x - 8$$ 6. **Convert to standard form:** Multiply both sides by 2 to clear the fraction: $$2y = 5x - 16$$ Rearranged: $$5x - 2y = 16$$ 7. **Cancel common factors if any:** None here. **Final answer:** The equation in standard form is $$5x - 2y = 16$$ This corresponds to option B.