Answer
The function of the graph passing through the point $\left( 3,\ -4 \right)$ and parallel to the line $3x-y-5=0$ is $y=3x-13$.
Work Step by Step
The equation of the line is $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$, where the point $\left( {{x}_{1}},\ {{y}_{1}} \right)=\left( 3,\ -4 \right)$.
The value of the slope $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$.
The equation is parallel to the line $y=3x-5$; the slope of the equation is $m=3$.
So, the equation is passing through the point $\left( {{x}_{1}},\ {{y}_{1}} \right)=\left( 3,\ -4 \right)$ is
$\begin{align}
& y-{{y}_{1}}=m\left( x-{{x}_{1}} \right) \\
& y+4=3\left( x-3 \right) \\
& y=3x-9-4 \\
& =3x-13
\end{align}$
