Algebra problem (2 probs)

(1)Let line L1 be the graph of 5x + 8y = -9 . Line L2  is perpendicular to line L1 and passes through the point (10,10). If line L2 is the graph of the equation y = mx + b, then find m + b.

The slope of the line in the form Ax + By  = C   is given by -A / B

So....the line 5x + 8y  = - 9   has the slope  -5/8

A perpendicular line to this one  will have a negative reciprocal slope  =  8/5

So......the equation for L2  with slope 8/5  = m  passing through (10, 10) = ( x1, y1) is

y   = m (x  - x1)  +  y1

y = (8/5) ( x - 10) + 10

y = (8/5)x - 16 + 10

y = (8/5)x  - 6

m =  8/5     and     b   =  -6

So

m +  b  =     8/5 - 6   =   8/5 - 30/5   =   - 22/5

EDIT TO CORRECT AN ERROR

(2) The perpendicular bisector of the line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB.

Find the equation of the perpendicular bisector of the line segment joining the points (1,2) and (7,4) Enter your answer in the form "y - mx + b."

The perpendicular line will pass through the midpoint  of  (1, 2)  and ( 7,4)

The midpoint is  [   ( 1 + 7)/ 2, (2 + 4) / 2 ]   =  [ 8/2, 6/2 ]  =  ( 4, 3)

The slope between  (1/2) and ( 7, 4)  is   [  4 - 2 ] / [ 7 - 1 ]  =  2 / 6   =  1 / 3

So....the slope of the pepenicular bisector  is   - 3

And the equation of the perpendicular bisector is

y  = - 3 ( x - 4) + 3

y =  -3x + 12 + 3

y = -3x + 15 

1.   Let's put this equation in to y = mx + b form (easier for me to visualize)

         5x + 8y = -9

           8y = -5x - 9

             y = -5/8  x   - 9/8     slope = -5/8

                 perpindicular slope = 8/5

   We know 10, 10 is on the new line....

      y = 8/5 (x) + b

      10 = (8/5) 10  + b      b = -6

      so     y = 8/5 x  - 6        m + b = -22/5