First out the equation 4x + 3y = -2 into slope-intercept form (y = mx + b).
4x + 3y = -2
Subtract 4x from both sides.
3y = -4x - 2
Divide all terms by 3.
y = -4/3x - 2/3
The slope in this equation is -4/3 (4 down, 3 to the right).
Using that slope, input the coordinates (5, 5) into the equation of a line:
y - y1 = m(x - x1)
y - 5 = -4/3(x - 5)
y - 5 = -4/3x + 20/3
y = -4/3x + 35/3
The equation of the line is y = -4/3x + 35/3.