Question 198888
Given Equation of the line is 2y + 7x = 14
=> 2y = - 7x +14
=> y = - (7/2) x +14 /2
=> y = (- 7 / 2) x + 7
now the above euation is of the form y= mx +c where m is slope and c as y intercept
The slope of the given line is   - 7/2
since the product of two perpendicular lines is -1
the slope of the line perpendicular to the given line must be 2/7
so the slope of the line perpendicular to the given line  is 2/7