#### Answer

$y \text{ is a function of }x
\\\text{Domain: }
\left( -\infty,6 \right)\cup (6,\infty)
\\\text{NOT a linear function}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To determine if the given equation, $
y=\dfrac{7}{x-6}
,$ is a function, check if $x$ is unique for every value of $y.$
To find the domain, find the set of all possible values of $x.$
A linear function is any equation that can be expressed as $f(x)=mx+b.$
$\bf{\text{Solution Details:}}$
For any $x,$ the quotient of $7$ and $x-6$ will produce only $1$ value of $y.$ Hence, $y$ is a function of $x.$
The denominator cannot be zero. Hence,
\begin{array}{l}\require{cancel}
x-6\ne0
\\\\
x\ne6
.\end{array}
The domain is the set of all real numbers except $6.$
Since the given equation cannot be expressed as $f(x)=mx+b,$ then it is not a linear function.
The given equation has the following characteristics:
\begin{array}{l}\require{cancel}
y \text{ is a function of }x
\\\text{Domain: }
\left( -\infty,6 \right)\cup (6,\infty)
\\\text{NOT a linear function}
.\end{array}