step 1
Find the slope of the given line
y=9x-3
the slope is m=9
step 2
Remember that
If two lines are perpendicular, then their slopes are negative reciprocal
that means
the slope of the perpendicular line is
m=-1/9
step 3
Find the equation of the line that is perpendicular to this line and passes through the point (-8, – 5).
we have
m=-1/9
point (-8,-5)
the equation in slope-intercept form
y=mx+b
substitute and solve for b
-5=(1/9)(-8)+b
-5=-(8/9)+b
b=-5+8/9
b=-37/9
y=-(1/9)x-37/9
step 4
Find the equation of the line that is parallel to this line and passes through the point (-8, -5).
Remember that
If two lines are parallel, then their slopes are equal
the slope of the parallel line is
m=9
the equation in slope-intercept form
y=mx+b
substitute and solve for b
-5=9(-8)+b
-5=-72+b
b=67
therefore
y=9x+67