step 1
Find the slope of the given line
we have
y=-4x-3
so
the slope is m=-4
step 2
Find the slope of the perpendicular line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the perpendicular line is
m=1/4
step 3
Find the equation of the line in slope-intercept form
y=mx+b
we have
m=1/4
point (3,3)
substitute
3=(1/4)(3)+b
solve for b
3=(3/4)+b
b=3-3/4
b=9/4
therefore
y=(1/4)x+9/4
the answer is the third option
