1. The problem asks to show that the coordinates of point C are (4, 0). 2. We are given the equation of the line in point-slope form: $$y - y' = m(x - x')$$ where $m$ is the slope and $(x', y')$ is a point on the line. 3. Substituting the given values: $$y - 0 = \frac{3}{2}(x - 4)$$ which simplifies to $$y = \frac{3}{2}(x - 4)$$. 4. To find the coordinates of C, we need to find the point where the line crosses the x-axis. On the x-axis, $y = 0$. 5. Substitute $y = 0$ into the equation: $$0 = \frac{3}{2}(x - 4)$$ 6. Multiply both sides by 2 to clear the fraction: $$0 = 3(x - 4)$$ 7. Divide both sides by 3: $$\cancel{\frac{0}{3}} = \cancel{\frac{3(x - 4)}{3}}$$ $$0 = x - 4$$ 8. Solve for $x$: $$x = 4$$ 9. Therefore, the coordinates of point C are $(4, 0)$ as required.