#### Answer

$\text{slope-intercept form: }
y=-3x+10
\\\\
\text{standard form: }
3x+y=10$

#### Work Step by Step

Using $y-y_1=m(x-x_1)$ or the point-slope form of linear equations, the equation of the line passing through $(
4,-2
)$ and with a slope of $m=
-3
$ is
\begin{array}{l}\require{cancel}
y-(-2)=-3(x-4)
\\\\
y+2=-3(x-4)
.\end{array}
In the form $y=mx+b$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y+2=-3(x-4)
\\\\
y+2=-3x+12
\\\\
y=-3x+12-2
\\\\
y=-3x+10
.\end{array}
In the form $Ax+By=C$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=-3x+10
\\\\
3x+y=10
.\end{array}
Hence, the different forms of the equation of the line with the given conditions are
\begin{array}{l}\require{cancel}
\text{slope-intercept form: }
y=-3x+10
\\\\
\text{standard form: }
3x+y=10
.\end{array}