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

Dec 6, 2016

The graph of this rectangular hyperbola (RH) is inserted. The vertical asymptote is $\uparrow x = - \frac{3}{2} \downarrow$ and the horizontal asymptote is $\leftarrow y = \frac{5}{2} \rightarrow$. The center of the RH is $C \left(- \frac{3}{2} , \frac{5}{2}\right)$.

#### Explanation:

Cross multiplying and reorganizing,

$\left(2 x + 3\right) \left(y - \frac{5}{2}\right) = - \frac{15}{2}$.

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

hyperbola.

This represents a hyperbola with asymptotes$x = - \frac{3}{2} \mathmr{and} y = - \frac{5}{2}$

meeting at the center $C \left(- \frac{3}{2} , \frac{5}{2}\right)$

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