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Find all values of \(a\) such that there is no value of \(b\) that satisfies the equation \(\frac{2-b}{3-b}=5a\).

 Feb 12, 2022
 #1
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2 - b

____  =     5a                     multiply both sides by  1/5

3  - b

 

( 2 - b )

_______  =     a

(15 - 5b)

 

Let  b =  x   and a =  y

 

( 2 - x)

_________  =      y         writing this  another way  we have

( 15   - 5x )

 

(-x + 2)

________      =  y

(-5x + 15)

 

Using  the coefficients on the x terms  we  note that   we have  the fraction   -x / -5x   =  1/5

 

This means that we have a horizontal asymptote     at  y = a =  1/5....i.e,  when a = 1/5 , there is no value of b that makes this true

 

Here's a graph to show this  :   https://www.desmos.com/calculator/zjrfinthwx

 

 

 

cool cool cool

 Feb 12, 2022
 #2
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Thanks!

Guest Feb 12, 2022

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