find the horizontal asymptote.\ny = \\frac{2x + 14}{x - 7}\ny = ?

Explanation:

Step1: Recall horizontal - asymptote rule

For a rational function $y=\frac{f(x)}{g(x)}=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, if $n = m$, the horizontal asymptote is $y=\frac{a_n}{b_m}$. Here, $f(x)=2x + 14$ (degree $n = 1$) and $g(x)=x - 7$ (degree $m = 1$).

Step2: Identify leading - coefficients

The leading coefficient of $f(x)$ is $a_n=2$ and the leading coefficient of $g(x)$ is $b_m = 1$.

Step3: Calculate the horizontal asymptote

Using the rule $y=\frac{a_n}{b_m}$, we have $y=\frac{2}{1}=2$.

Answer:

$y = 2$