has parallel lines with the same slope =2/3
= the coefficient of the x term when the linear equation is solved for y
y=2/3x +b where b= any number except -4. if b=-4, it's not a parallel line. it's the same identical line
to go through the point (6,7) preplace x ith 6 and y with 7. then solve for b.
7= 2(6)/3 + b
b = 7-4=3
the parallel line is y=2/3x +3
That's the likely answer you want.
if you meant y= (2/3)x-4 as the given line
But there's an ambiguity to the problem
as written it really says y = 2/(3x) -4
or possibly it even meant y= 2/(3x-4)
both these alternatives are rectangular hyperbolas,
with curved hyperbolic lines as the parallel lines
y= 2/(3x) -4 has slope = the derivative = y'
y = 2/(3x)-4 = (2/3)x^-1 -4
y' = -2/(3x^2)
a hyperbolic line with that slope would be the parallel line
it would be helpful to graph the hyperola, to see the lines better
the parallel line is y=2/(3x) +98/9 in order to go through (6,7).
just the same basic rectangular hyperbola
shifted vertically up by 10 8/9=98/9
that's technically the correct answer to the problem as written