Find the slope of the line which is perpendicular to the line connecting the points A(- 5, 3) and B(2, 6)

Correct option is D

Step 1: Find the slope of the line connecting points A and B

The formula for the slope m between two points $$x_1, y_1$$​ and $$x_2, y_2$$​ is:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$​
Substitute $$(x_1, y_1)$$​ = (-5, 3) and $$(x_2, y_2)$$​ = (2, 6):
$$m = \frac{6 - 3}{2 - (-5)} = \frac{3}{7}$$​

Step 2: Find the slope of the perpendicular line.
The slope of a line perpendicular to another is the negative reciprocal of the original slope. If the slope of the original line is m, the slope of the perpendicular line is:
$$m_\text{perpendicular} = -\frac{1}{m}$$​

Substitute $$m = \frac{3}{7}$$​
$$m_\text{perpendicular} = -\frac{1}{\frac{3}{7}} = -\frac{7}{3}$$​

Final Answer:

The slope of the line perpendicular to the line connecting A and B is:
$$m_\text{perpendicular} = -\frac{7}{3}$$​