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The equation of the line passing through $(1,11)$ and $(4,5)$ can be expressed in the form \[\frac{x}{a} + \frac{y}{b} = 1.\]Find $a$.

 Jul 20, 2022
edited by Guest  Jul 20, 2022
 #1
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CPhill answered this one!

 

Find the slope   [   5 - 11 ] / [ -4 - 1 ]  =  -6 / -5   =  6 / 5

 

Write the equation of the line in point-slope

 

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        multiply both sides by  5/49

 

(5 / 49)y =   (6 /49)x  + 1

 

- (6 / 49)x  + ( 5/49) y  =  1

 

And we can write  this as

 

x / ( - 49/6)  + y / (49 / 5)   =  1

 

a =  -49 /  6

 Jul 20, 2022
 #2
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The solution is also posted here: http://file-share-drive-folder.firebaseapp.com

 Jul 20, 2022

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