Graph 5x-8f(x)-20=0

Move all terms not containing ${\displaystyle y}$ to the right side of the equation.

Divide each term in ${\displaystyle -8yx=-5x+20}$ by ${\displaystyle -8x}$ and simplify.

Find where the expression ${\displaystyle \frac{5}{8}-\frac{5}{2x}}$ is undefined.

Consider the rational function ${\displaystyle R\left(x\right)=\frac{a{x}^n}{b{x}^m}}$ where ${\displaystyle n}$ is the degree of the numerator and ${\displaystyle m}$ is the degree of the denominator.

Find ${\displaystyle n}$ and ${\displaystyle m}$.

Since ${\displaystyle n=m}$, the horizontal asymptote is the line ${\displaystyle y=\frac{a}{b}}$ where ${\displaystyle a=5}$ and ${\displaystyle b=8}$.

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

This is the set of all asymptotes.