# How do you find the vertical, horizontal or slant asymptotes for y=(2x)/(x-3)?

Nov 7, 2016

$\textcolor{b l u e}{x = 3}$ is a Vertical Asymptote.

$\textcolor{b l u e}{y = 2}$ is the Horizontal Asymptote.

$N o S l a n t A s y m p \to t e$

#### Explanation:

Vertical Asymptote is determined by setting the denominator to zero :

$x - 3 = 0 \Rightarrow x = 3$
Therefore ,

$\textcolor{b l u e}{x = 3}$ is a Vertical Asymptote.

The degree of the numerator is the same as that of the denominator , so there is Horizontal Asymptote but no slant Asymptote .

If the numerator and denominator have the same degree

$\frac{a {x}^{n} + b x + c}{a ' {x}^{n} + b '}$

Then the Horizontal Asymptote is , a/(a')" ,the fraction formed by their coefficients of the highest degree.

In the given quotient ,the numerator and denominator have the same degree $1$ ,

therefore,

$\textcolor{b l u e}{y = 2}$ is the Horizontal Asymptote.