Question

If the graph of y=(ax-5)/(x+b)
does not intersect either of the lines x=7 or y=−3 , what is the value of a and b ?

Answer 1

so x=7 must be a vertical asymptote, which means
the denominator must be x-7 or b = -7

so now we have y = (ax-5)/(x-7)
let's see if y = -3
-3 = (ax-5)/(x-7)
-3x + 21 = ax - 5
ax + 3x = 26
x(a+3) = 26
x = 26/(a+3) , for that to be undefined, a = -3

y = (-3x - 5)/(x-7)

check:
http://www.wolframalpha.com/input/?i=plot+y+%3D+%28-3x+-+5%29%2F%28x-7%29