#### Answer

$\text{Slope-Intercept Form: }
y=-\dfrac{1}{4}x-1
\\\text{Standard Form: }
x+4y=-4$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the equation of the line with the following properties:
\begin{array}{l}\require{cancel}
\text{Slope: }
-\dfrac{1}{4}
\\\text{$y$-intercept: }
(0,-1)
,\end{array}
use the Slope-Intercept Form of linear equations. Give the equation in the Slope-Intercept Form and in the Standard Form.
$\bf{\text{Solution Details:}}$
With the given properties, then $
m=-\dfrac{1}{4}
$ and $
b=-1
.$ Using $y=mx+b$ (where $m$ is the slope and $b$ is the $y$-intercept) or the Slope-Intercept Form of linear equations, then the equation of the line is
\begin{array}{l}\require{cancel}
y=mx+b
\\\\
y=-\dfrac{1}{4}x+(-1)
\\\\
y=-\dfrac{1}{4}x-1
.\end{array}
Using the properties of equality, in the form $ax+by=c$ or the Standard Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
4(y)=4\left( -\dfrac{1}{4}x-1 \right)
\\\\
4y=-x-4
\\\\
x+4y=-4
.\end{array}
The equation of the line is
\begin{array}{l}\require{cancel}
\text{Slope-Intercept Form: }
y=-\dfrac{1}{4}x-1
\\\text{Standard Form: }
x+4y=-4
.\end{array}