Answer
$\text{slope-intercept form: }
y=3x-19
\\\\
\text{standard form: }
3x-y=19$
Work Step by Step
In the slope-intercept form, the given equation, $
3x-y=8
,$ is equivalent to
\begin{array}{l}\require{cancel}
-y=-3x+8
\\\\
y=3x-8
.\end{array}
Hence, the slope of this line is $
3
.$
Since the line passing through the given point, $(
7,2
),$ is parallel to the previous line, then the slopes of these lines are equal. Using $y-y_1=m(x-x_1)$ or the point-slope form, the equation of the line is
\begin{array}{l}\require{cancel}
y-2=3(x-7)
.\end{array}
In $y=mx+b$ form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-2=3x-21
\\\\
y=3x-21+2
\\\\
y=3x-19
.\end{array}
In $Ax+By=C$ form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
-3x+y=-19
\\\\
3x-y=19
.\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-19
\\\\
\text{standard form: }
3x-y=19
.\end{array}
