Find all values of \(a\) such that there is no value of \(b\) that satisfies the equation \(\frac{2-b}{3-b}=5a\).
+128408 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
