1. **State the problem:** Find the equation of the straight line passing through the points $(5, 10)$ and $(9, 24)$ in the form $y = mx + c$. 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:** $$m = \frac{24 - 10}{9 - 5} = \frac{14}{4} = \frac{\cancel{14}}{\cancel{4}} \times \frac{7}{2} = 7/2$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Using point $(5, 10)$: $$y - 10 = \frac{7}{2}(x - 5)$$ 5. **Expand and simplify:** $$y - 10 = \frac{7}{2}x - \frac{7}{2} \times 5 = \frac{7}{2}x - \frac{35}{2}$$ 6. **Add 10 to both sides:** $$y = \frac{7}{2}x - \frac{35}{2} + 10$$ Convert 10 to fraction with denominator 2: $$10 = \frac{20}{2}$$ 7. **Combine constants:** $$y = \frac{7}{2}x - \frac{35}{2} + \frac{20}{2} = \frac{7}{2}x - \frac{15}{2}$$ **Final answer:** $$y = \frac{7}{2}x - \frac{15}{2}$$ This is the equation of the line in slope-intercept form.