1. **Problem statement:** Find the equation of the line passing through points $A(5,-2)$ and $B(7,3)$. 2. **Formula:** 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 line equation in point-slope form is: $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope:** $$m=\frac{3 - (-2)}{7 - 5} = \frac{3 + 2}{2} = \frac{5}{2}$$ 4. **Write the line equation using point A:** $$y - (-2) = \frac{5}{2}(x - 5)$$ $$y + 2 = \frac{5}{2}x - \frac{25}{2}$$ 5. **Simplify to slope-intercept form:** $$y = \frac{5}{2}x - \frac{25}{2} - 2$$ $$y = \frac{5}{2}x - \frac{25}{2} - \frac{4}{2}$$ $$y = \frac{5}{2}x - \frac{29}{2}$$ 6. **Check if point $(4,-4)$ lies on the line:** Substitute $x=4$: $$y = \frac{5}{2} \times 4 - \frac{29}{2} = 10 - 14.5 = -4.5$$ Since $-4.5 \neq -4$, point $(4,-4)$ is not on the line. **Final answers:** - Slope $m = \frac{5}{2}$ - Equation: $$y = \frac{5}{2}x - \frac{29}{2}$$ - Point $(4,-4)$ is not on the line.