ANSWER
[tex]- \frac{6}{7} [/tex]
EXPLANATION
The given points are
[tex](x_1,y_1)=(7,4)[/tex]
and
[tex](x_2,y_2)=(1,-3)[/tex]
The formula for finding the slope is given by,
[tex]slope = \frac{y_1-y_1}{x_1-x_1} [/tex]
We substitute the points to obtain,
[tex]slope = \frac{ - 3 - 4}{1 - 7} = \frac{7}{6} [/tex]
The slope of the line that is perpendicular to DE is the negative reciprocal of
[tex]\frac{7}{6} [/tex]
Thus, the line perpendicular to DE has slope,
[tex] \frac{ - 1}{ \frac{ 7}{6} } =-\frac{6}{7} [/tex]
