find the horizontal asymptote.\ny = \\frac{6x - 24}{2x + 12}\ny = ?

Explanation:

Step1: Identify degrees of polynomials

The numerator $6x - 24$ is a first - degree polynomial and the denominator $2x+12$ is a first - degree polynomial.

Step2: Use horizontal asymptote rule for equal - degree polynomials

For a rational function $y=\frac{a_nx^n+\cdots+a_0}{b_nx^n+\cdots + b_0}$ where $n$ is the degree of both the numerator and denominator, the horizontal asymptote is $y = \frac{a_n}{b_n}$. Here $a_n = 6$ and $b_n=2$. So, $y=\frac{6}{2}$.

Step3: Simplify the result

$y = 3$.

Answer:

$y = 3$