When a line passes through the two points [tex] (x_{1},y_{1}) and (x_{2},y_{2}) [/tex] , its slope is given by the formula [tex] m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
In this question, a line L passes through the points [tex] (1,1) and (7,8) [/tex]
So, its slope is given by [tex] m=\frac{8-1}{7-1} [/tex]
[tex] m=\frac{7}{6} [/tex]
When two lines are perpendicular, then the product of their slopes is -1.
Since, the slope of the line L is [tex] \frac{7}{6} [/tex] , so the slope of the line which is perpendicular to the given line L is [tex] \frac{-6}{7} [/tex] as the product of [tex] \frac{-6}{7} \times \frac{7}{6}=-1 [/tex].
