The image of the point with coordinates (1,1) under the reflection across the line y=mx+b is the point with coordinates (9,5). Find m+b.

The midpoint of the line connecting these two points will lie on the line we seek...and this is

[ (1 + 9 ) / 2, ( 1 + 5) / 2 ]  =  [ 5, 3 ]

And the slope of this line connecting the given points is  [ 5 - 1 ] / [ [ 9 - 1]  = 4/8  =  1/2

And the line we seek is perpendicular to this line...so its slope is  - 2

And the equation of this line  is

y = -2 (x - 5) + 3

y = - 2x  + 10 + 3

y  = - 2x + 13

So...m  +  b  =   -2 + 13   =  11 

Here's a pic :  https://www.desmos.com/calculator/jdelhysrdy