Aline passes through (9, –9) and (10, –5). a. write an equation for the line in point-slope form. b. rewrite the equation in standard form using integers. y + 9 = 4(x – 9); –4x + y = –45 y – 9 = 4(x + 9); –4x + y = 45 y – 9 = 4(x – 9); –4x + y = 45 y + 9 = 4(x + 9); –4x + y = –45

bearing in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb