The slope of a line perpendicular to the line passing through the points (2, 5) and (-3, 6) is

1. $-\dfrac{1}{5}$

2. $\dfrac{1}{5}$

3. -5

4. 5

Slope (m₁) of line joining the points (2, 5) and (-3, 6) is given by

$= \dfrac{y$2 - y1}{x_2 - x1} \\[1em] = \dfrac{6 - 5}{-3 - 2} \\[1em] = -\dfrac{1}{5}.

Let slope of perpendicular line be m₂. Then,

$\Rightarrow m$1 \times m2 = -1 \\[1em] \Rightarrow -\dfrac{1}{5} \times m2 = -1 \\[1em] \Rightarrow m2 = 5.

∴ Slope of line perpendicular to this line = 5.

Hence, Option 4 is the correct option.