APPENDIX B - Coordinate Geometry and Lines - B Exercises - Page A 15: 7

$2$

To find the slope of the line passing through $(1,5)$ and $(4,11)$, we use the slope formula: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. Plug in the given values of $x$ and $y$: $m=\frac{11-5}{4-1}$. Simplify to arrive at the answer: $m=\frac{6}{3}=2$.