Answer
$y = -2/3*x +10/3$
Work Step by Step
Parallel to $2x+3y =9$ and through (-1, 4)
$2x+3y = 9$
$2x+3y -3y-9 = 9 - 3y - 9$
$2x-9 = -3y$
$-1/3*(2x-9) = -3y/-3$
$-2/3*x + 3 = y$
$y = -2/3*x +3$
The parallel line would have the same slope (-2/3).
$4 = -2/3*(-1)+b$
$4 = 2/3 +b$
$4-2/3 = 2/3 + b - 2/3$
$10/3 = b$
$y = -2/3*x +10/3$
