1. **State the problem:** Find the equation of the line joining the points (4,1) and (7,3). 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line in point-slope form is $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope:** $$m = \frac{3 - 1}{7 - 4} = \frac{2}{3}$$ 4. **Write the point-slope form using point (4,1):** $$y - 1 = \frac{2}{3}(x - 4)$$ 5. **Expand and simplify:** $$y - 1 = \frac{2}{3}x - \frac{8}{3}$$ 6. **Add 1 to both sides:** $$y = \frac{2}{3}x - \frac{8}{3} + 1$$ 7. **Convert 1 to fraction with denominator 3:** $$1 = \frac{3}{3}$$ 8. **Combine constants:** $$y = \frac{2}{3}x - \frac{8}{3} + \frac{3}{3} = \frac{2}{3}x - \frac{5}{3}$$ **Final answer:** $$y = \frac{2}{3}x - \frac{5}{3}$$