The points (3,24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function? A) A 50-page photo album holds 400 photographs.

B) An 80-page photo album holds 560 photographs.

C) A 100-page photo album holds 8,000 photographs.

D) A 900-page photo album holds 8,400 photographs.

the answer to the question is a  

it has the same slope and the same y-intercept.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)