find the equation of the line that goes through (-6,8) and is perpendicular to y=-3/2x-4
step 1
Find teh slope of the given line
y=(3/2)x-4
the slope is m=3/2
Remember that, if two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the perpendicular line is
m=-2/3
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-2/3
point (-6,8)
substitute the given values
8=-(2/3)*(-6)+b
solve for b
8=4+b
b=4
therefore
the equation of the perpendicular line is
y=-(2/3)x+4