Answer
(H) $y=\frac{1}{4}x-5$.
Work Step by Step
The given point is
$\Rightarrow (x_1,y_1)=(8,-3)$
Perpendicular line:
$\Rightarrow y=-4x+5$
It is in slope-intercept form $y=mx+c$.
The slope of the equation is $m=−4$
Perpendicular lines have slopes that are negative reciprocals of one another.
The slope of the required line is
$\Rightarrow m=\frac{1}{4}$
The equation of the line is
$\Rightarrow y−y_1=m(x−x_1)$
Substitute all values into the point-slope equation.
$\Rightarrow y−(-3)=(\frac{1}{4})(x−8)$
Simplify.
$\Rightarrow y+3=\frac{1}{4}x−2$
$\Rightarrow y=\frac{1}{4}x−2-3$
$\Rightarrow y=\frac{1}{4}x−5$
Hence, the correct option is (H) $y=\frac{1}{4}x-5$.
