3x +4y = -14
4y = -3x - 14
y = -(3/4)x - 14/4
y= -(3/4)x -7/2
The slope of this line = -3/4
The slope ofthe perpendicular line = 4/3
So...using the slope and point (-5, 7) we have
y = (4/3) ( x - - 5) + 7
y= (4/3)( x + 5) + 7
y= (4/3)x + 20/3 + 21/3
y= (4/3)x + 41/3
m + b = 4/3 + 41/3 = 45/3 = 15
Here's a graph : https://www.desmos.com/calculator/uxagghudww