y = Four-thirds x – 8
Step-by-step explanation:
Step 1:
First step is to find the slope of the line joining the 2 given points
(negative 4, 4) and (4, negative 2).
Formula for finding the slope of the line joining 2 given points is
Slope m = (change in y)/(change in x)
Using the above formula , the slope of the line joining the 2 given points
is m = (-2-4)/(4-(-4)) = -6/8 =-3/4
Step 2 :
Find the slope of the line perpendicular to the line joining the 2 given
points
Slopes of 2 perpendicular lines are negative reciprocals of each other
, i.e if m1 and m2 are slopes of 2 lines then m1*m2 = -1, if the lines are
perpendicular to each other.
Hence the slope of the line perpendicular to the line joining the above 2
given points is
m1*m2 = -1 => (-3/4)*m2 = -1 => m2 = 4/3
Step 3 :
Find the equation of the line with slope 4/3 and has an x- intercept of 6
X intercept of 6 means the line passes through the point (6,0)
Equation of a line passing through a given point and having a slope
of m is (y - y1) = m(x-x1).
Substituting slope as m= 4/3 and point (x1,y1) as (6,0) in the above
equation,
(y-0) = (4/3)(x-6)
=> y = (4/3)x - (4/3)*6
=> y = (4/3)x - 8
Hence the required answer is y = (4/3)x - 8
