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The equation of the line passing through (1,11) and (-4,5) can be expressed in the form x/a + y/b = 1. Find a.

 Apr 12, 2022
 #1
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x/a  +  y/b  =  1              manipulate as follows

 

bx + ay  =   ab

 

ay =  -bx  + ab

 

y  = (-b/a)x  +  b         (1)

 

The slope of the given line  =  [ 5 -11] / [ -4 - 1]   =   [-6] / [-5]   = 6/5

 

The equation of this  line  can be written  as

 

y = (6/5) ( x - 1)  + 11

 

y = (6/5)x  - 6/5 + 11

 

y  = (6/5)x -6/5 + 55/5

 

y = (6/5)x + 49/5       (2)

 

Comparing  (1) and (2),  b =  49/5

 

So

 

-b /a  =  6/5

 

(-49/5) / a  = 6/5

 

-49/a = 6

 

a = -49/6

 

 

cool cool cool

 Apr 12, 2022

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