Answer
The equation of the line is $y=4x-17$.
Work Step by Step
The general slope–intercept form of the line is given by:
$y-{{y}_{0}}=m\left( x-{{x}_{0}} \right)$
The line is passing through the point $\left( 3,-5 \right)$ and the slope is the negative reciprocal of $-\frac{1}{4}$. So the slope of the line is 4.
Now, substitute $\left( {{x}_{0}},{{y}_{0}} \right)=\left( 3,-5 \right)$ and $m=4$ in equation as shown below:
$\begin{align}
& y+5=4\left( x-3 \right) \\
& y+5=4x-12 \\
& y=4x-12-5 \\
& y=4x-17
\end{align}$
Hence, the slope–intercept form of the line is given by
$y=4x-17$.
