Write an equation for a line that's perpendicular to y =(2/3)x+5
and passes through (4, -6).
step 1
Find the slope of the perpendicular line
we have the slope of the given line, m=2/3
Remember that, if two lines are perpendicular, then the product of their slopes is equal to -1 (are inverse reciprocal)
so
the slope of the perpendicular line is
m=-3/2
step 2
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-3/2
(x1,y1)=(4,-6)
substitute
y+6=(-3/2)(x-4)
Convert to slope intercept form
y=mx+b
isolate the variable y
y+6=(-3/2)x+6
y=(-3/2)x
or
y=-1.5x