#### Answer

$\text{a) Slope-Intercept Form: }
y=14
\\\\\text{b) Standard Form: }
y=14$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the equation of the line with the given characeristics:
\begin{array}{l}\require{cancel}
\text{through }
(-3,14)
\\
\text{horizontal}
,\end{array}
use the Point-Slope Form of linear equations. Express the answer in Slope-Intercept Form and in the Standard Form.
$\bf{\text{Solution Details:}}$
Horizontal lines have a slope of $0$. Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions,
\begin{array}{l}\require{cancel}
y_1=14
,\\x_1=-3
,\\m=0
,\end{array}
is
\begin{array}{l}\require{cancel}
y-y_1=m(x-x_1)
\\\\
y-14=0(x-(-3))
\\\\
y-14=0
.\end{array}
In the form $y=mx+b$ or the Slope-Intercept Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-14=0
\\\\
y-14=0x
\\\\
y=0x+14
\\\\
y=14
.\end{array}
In the form $ax+by=c$ or the Standard Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=14
.\end{array}
Hence, the equation of the line is
\begin{array}{l}\require{cancel}
\text{a) Slope-Intercept Form: }
y=14
\\\\\text{b) Standard Form: }
y=14
.\end{array}