Find an equation of a rational function with the following characteristics:

x-int of 5, y-int of -5/8, vertical asymptote x=-8/5, horizontal asymptote y=1/3

What is a possible answer and how did you arrive at each step?

2 answers

vertical asymptote
y = a/(5x+8)

x-int
y = a(x-5)/(5x+8)

horizontal asymptote
y = (5/3)(x-5)/((5x+8)) = (5x-25)/(15x+24)

This has a y-intercept of -25/24
So, how will you adjust it to get -5/8?

you want y(0) = -5/8, so
How would I continue from there?