step 1
Find out the slope of the line that passes through the points (-2,1) and (6,7)
m=(7-1)/(6+2)
m=6/8
m=3/4
step 2
Find out the slope of the perpendicular line
Remember that
If two lines are perpendicular
then
their slopes are negative reciprocal
therefore
The slope of the perpendicular line is
m=-4/3
step 3
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=-4/3
point (-6,9)
substitute and solve for b
9=-(4/3)(-6)+b
9=8+b
b=1
therefore
The equation of the line is
y=-(4/3)x+1