Answer
$f(x)=-\frac{1}{4}x-6$.
Work Step by Step
The given perpendicular line equation is
$\Rightarrow 4x-y=6$
The slope-intercept form is
$\Rightarrow y=4x-6$
Slope of the above line is $m_1=4$
and $y-$intercept is $-6$
Two lines are perpendicular if their slopes are negative reciprocal to each other.
Hence, slope of the perpendicular line
$\Rightarrow m_2=−\frac{1}{m_1}$
$\Rightarrow m_2=−\frac{1}{4}$
$y-$ intercept is same for both lines
Hence, the $y-$ intercept for the required line is $-6$.
The standard slope-intercept form is
$\Rightarrow y=mx+c$
Plug all values.
$\Rightarrow y=(-\frac{1}{4})x-6$
Plug $y=f(x)$.
$\Rightarrow f(x)=-\frac{1}{4}x-6$.
