Verified answer

If you have had a good precalc course then you would know the answer

is | 6(4) + 3 (-5) + 4 | / √ (4² + {-5}² )...if not but you have some calculus then form the distance function

from (4 , -5 ) to (x,y) { on the line }...s = √ ( [x-4]² + [ (- 4 - 6x ) / 3 - (-5)]² ) and minimize

it is easier with s²

Any factor to line -2x+3y+4 =0 has coordinates: (x, (2x-4)/3 ) enable be a cellular factor M (x, (2x-4)/3 ) to this line Distance D between factor (4, -5) and M is: D^2 = (x-4)^2 + ((2x-4)/3 + 5)^2 = x^2 - 8x + sixteen + (2x+ 11)^2 / 9 = (a million+4/9)x^2 - x(8 - 40 4/9) + sixteen + 121/9 = (13/9)x^2 - (28/9)x + 265/9 For x = (28/9)/(2*13/9) = (28/9)*(9/26) = 14/13 you have a interior of sight minimum for this parabola For x = 14/13 you get y = (2*(14/13)-4)/3 = (28/13- fifty two/13)/3 = -8/13 Closest factor is (x,y) = (14/13, -8/13)