Answer
$$
y=\frac{3-2x}{4x+20}
$$
We obtain that :
Asymptotes: $y=-\frac{1}{2} $ and $ x=-5$
$x$-intercept: $\frac{3}{2}$ the value when $y= 0$.
$y$-intercept: $\frac{3}{20}$ the value when $x= 0$
Work Step by Step
$$
y=\frac{3-2x}{4x+20}
$$
The value $ x=-5$makes the denominator 0, but not the numerator, so the line $ x=-5$ is a vertical asymptote.
To find a horizontal asymptote, let x get larger and we obtain :
$$
y=\lim\limits_{x \to \infty}\frac{3-2x}{4x+20}=-\frac{1}{2}
$$
This means that the line $y=-\frac{1}{2} $ is a horizontal asymptote.
So, we have:
Asymptotes: $y=-\frac{1}{2} $ and $ x=-5$
$x$-intercept: $\frac{3}{2}$ the value when $y= 0$.
$y$-intercept: $\frac{3}{20}$ the value when $x= 0$
