Step 1
Find the slope of the given line
Let
[tex]A(-4,4)\ B(4,-2)[/tex]
we know that
the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-2-4}{4+4}[/tex]
[tex]m=\frac{-6}{8}[/tex]
[tex]m=-\frac{3}{4}[/tex]
Step 2
Find the slope of the line perpendicular to the given line
we know that
if two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=-\frac{3}{4}[/tex] ------> slope of the given line
Find the value of m2
[tex]m2=-1/m1[/tex]
substitute
[tex]m2=-1/(-3/4)[/tex]
[tex]m2=\frac{4}{3}[/tex]
Step 3
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{4}{3}[/tex]
x-intercept is equal to [tex]6[/tex] --------> is the point [tex](6,0)[/tex]
substitute in the formula
[tex]y-0=\frac{4}{3}(x-6)[/tex]
[tex]y=\frac{4}{3}x-8[/tex]
therefore
the answer is the option
[tex]y=\frac{4}{3}x-8[/tex]
