Given:
The line through (6, −3) and (7, 6) is perpendicular to the line through (−2, 5) and (x, −1).
To find:
The value of x.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is:

The slope of the line through (6, −3) and (7, 6) is:



The slope of the line through (−2, 5) and (x, −1) is:


We know that the product of slopes of two perpendicular lines is -1.



Multiplying both sides by (x+2), we get




Divide both sides by -1.

Therefore, the value of x is 52.