How do you find the asymptotes for $y = \frac{7 x - 5}{2 - 5 x}$ $y = (7x-5)/(2-5x)$ ?

Question

1934 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-22T07:43:42

The asymptotes are $x = \frac{2}{5}$ $x=2/5$ vertical asymptote
$y = - \frac{7}{5}$ $y=-7/5$ horizontal asymptote

Take the limit of y as x approaches $\infty$ $oo$

$lim_(x->oo) y=lim_(x->oo) (7x-5)/(-5x+2)=lim_(x->oo) (7-5/x)/(-5+2/x)=-7/5$

$x=-7/5$

Also if you solve for x in terms of y,

$y=(7x-5)/(-5x+2)$

$y(-5x+2)=7x-5$

$-5xy+2y=7x-5$

$2y+5=7x+5xy$

$2y+5=x(7+5y)$

$x=(2y+5)/(5y+7)$

take now the limit of x as y approaches $oo$

$lim_(y->oo) x=lim_(y->oo) (2y+5)/(5y+7)=lim_(y->oo) (2+5/y)/(5+7/y)=2/5$

$y=2/5$

kindly see the graph.

graph{y=(7x-5)/(-5x+2)[-20,20,-10,10]}

have a nice day!

How do you find the asymptotes for y = (7x-5)/(2-5x)y=7x−52−5xy = (7x-5)/(2-5x)?