Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).

Point point form for the line through (a,b) and (c,d) is

(c-a)(y-b) = (d-b)(x-a)

We don't care about the constant part, this is

(b-d)x + (c-a)y = some constant

(a,b)=(5,-1) and (c,d)=(2,-5)

(-1 - -5) x + (2 - 5)y = some constant

4x - 3y = some constant

We didn't bother to calculate to constant because the parallel through (-1,8) means we get a different constant, obviously

4x - 3y = 4(-1) - 3(8)

4x - 3y = -28

i think is g(1)=-1.

hope that i can

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1