#### Answer

$\text{Slope-Intercept Form: }
y=-4x+15
\\\text{Standard Form: }
4x+y=15$

#### Work Step by Step

Use the Point-Slope Form of linear equations to find the equation of the line passing through $(
4,-1
)$ and with $m=
-4
.$
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 is
\begin{array}{l}\require{cancel}
y-(-1)=-4(x-4)
\\\\
y+1=-4(x-4)
.\end{array}
Using $y=mx+b$ or the Slope-Intercept Form of linear equations, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y+1=-4x+16
\\\\
y=-4x+16-1
\\\\
y=-4x+15
.\end{array}
Using $Ax+By=C$ or the Standard Form of linear equations, the equation above is equivalent to
\begin{array}{l}\require{cancel}
4x+y=15
.\end{array}
Hence, the equation of the line is
\begin{array}{l}\require{cancel}
\text{Slope-Intercept Form: }
y=-4x+15
\\\text{Standard Form: }
4x+y=15
.\end{array}