Answer :
Let line m passes through the point (7,5) and be perpendicular to the line 2x - 3y =6
Let AB be the line having equation 2x - 3y = 6
Therefore, slope of line AB = -a/b .......Formula
Slope = -2/-3 = 2/3
Therefore, slope of line m = -1/ 2/3 = -3/2
By using Slope-Point form of the line, equation of the line m is,
y - y1 = m (x - x1)
y - 5 = -3/2 (x - 7)
2(y - 5) = -3 ( x - 7)
2y - 10 = -3x + 21
3x + 2y = 31
Therefore, equation of the line is 3x + 2y + 31