Vertical Asyn of (x+1) Horizontal of 3/4 and Y intercept of 2 what is the equation?

Question

For my math question is rational equations I am given the vertical asymptote and the horizontal and and y intercept I am asked to determine an equation but the horizontal asymptote is throwing me off. VA = (x+1) HA= (3/4) Y= 2 what would the eqution be?

Answer 1

The equation can be of the form y=(ax+b)/(cx+d).

cx+d=0 when x=1 (not x+1), so c+d=0, making d=-c. (y=x+1 is not vertical.)

The horizontal asymptote is found by replacing x with a large value X, so y=(aX+b)/(cX+d)=aX/cX=a/c when X is very large, so a/c=¾, so 4a=3c and c=4a/3.

The y-intercept is found by setting x=0: b/d=2, making d=b/2.

Since d=-c=-4a/3, and d=b/2, b/2=-4a/3, so b=-8a/3.

If a=3, b=-8, c=4 and d=-4, making y=(3x-8)/(4x-4). The graph is shown below (green), and its asymptotes are shown in red.