Answer
$4x-y=12$
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 $(
3,0
)$ and with a slope of $m=
4
$ is
\begin{array}{l}\require{cancel}
y-0=4(x-3)
\\\\
y=4(x-3)
.\end{array}
In the form $y=mx+b$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=4(x-3)
\\\\
y=4x-12
.\end{array}
In the form $Ax+By=C$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=4x-12
\\\\
-4x+y=-12
\\\\
4x-y=12
.\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=4x-12
\\\\
\text{standard form: }
4x-y=12
.\end{array}
