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# Algebra problem (2 probs)

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(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.

(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."

This is just a new topic and these are some of the example problems on my sheet, its very new and confusing to me thanks for the help!

Nov 11, 2018

#1
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(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   Nov 11, 2018
edited by CPhill  Nov 11, 2018
#2
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(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   Nov 11, 2018
#3
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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

Nov 11, 2018
edited by ElectricPavlov  Nov 11, 2018