Question

How do you graph `y=(5x)/(2x+3)` using asymptotes, intercepts, end behavior?

Answer 1

The graph of this rectangular hyperbola (RH) is inserted. The vertical asymptote is `uarr x =-3/2 darr` and the horizontal asymptote is `larr y = 5/2 rarr`. The center of the RH is `C(-3/2, 5/2)`.

Explanation:

Cross multiplying and reorganizing,

`(2x+3)(y-5/2)=-15/2`.

Comparing with the form (ax+by+c)(lx+my+n)=constant for a

hyperbola.

This represents a hyperbola with asymptotes`x =-3/2 and y =-5/2`

meeting at the center `C(-3/2, 5/2)`

graph{(2x+3)(y-5/2)+15/2=0 [-20, 20, -10, 10]}