Let line $l_1$ be the graph of $5x + 8y = -9$. Line $l_2$ is perpendicular to line $l_1$ and passes through the point $(10,10)$. If line $l_2$ is the graph of the equation $y=mx +b$, then find $m+b$.
5x + 8y = -9 subtract 5x from both sides
8y = -5x - 9 divide both sides by 8
y = (-5/8)x - (9/8)
The slope of this line is -5/8
So.....the slope of a perpendicular line is 8/5
Since this line passes through (10,10) we have that
y = (8/5) (x - 10) +10 simplify
y = (8/5)x - 80/5 + 50/5
y= (8/5) x - 30/5
m = 8/5 b = -30/5
So
m + b = -22/ 5