find the horizontal asymptote.\n\n$$y = \\frac{4x - 12}{x + 2}$$\n\n$$y = ?$$

Explanation:

Step1: Identify the degrees of the numerator and denominator

The degree of the numerator $4x - 12$ is $1$, and the degree of the denominator $x + 2$ is $1$.

Step2: Apply the horizontal asymptote rule

Since the degrees are equal, the asymptote is the ratio of the leading coefficients. $$y = \frac{a_n}{b_n}$$

Step3: Calculate the ratio of the leading coefficients

The leading coefficient of the numerator is $4$ and the denominator is $1$. $$y = \frac{4}{1} = 4$$

Answer:

y = 4