# How do you find the vertical, horizontal or slant asymptotes for y = 5/(x - 1)?

Nov 23, 2016

Horizontal asymptote: $y = 0$

#### Explanation:

The only horizontal/slant asymptote is a horizontal asymptote at $y = 0$. This is because the degree on the numerator (0) is less than the degree on the denominator (1).

Nov 23, 2016

Vertical asymptote: x = 1; and horizontal asymptote: y = 0.

#### Explanation:

graph{y(x-1)-5=0 [-10, 10, -5, 5]}

The general equation of a rectangular hyperbola with center at (

alpha, beta ) and m as the slope of one of the asymptotes is

((y-beta)-m(x-alpha)((m(y-beta)+x-alpha) = constant.

The asymptotes are given by

$y - \beta = m \left(x - \alpha\right) \mathmr{and} x - \alpha + m \left(y - \beta\right) = 0$

Here, it is $y \left(x - 1\right) = 5$. So, the asymptotes are given by

x-1=0 and y = 0.

For this answer, I recalled from my memory what I had learnt, more

than 60 years ago. The graph affirms that I am right.