Question

A company makes jewelry. It costs $6,400 to make 10 pieces of jewelry and $11,200 to make 20 pieces of jewelry. Which equation models the cost, C(x), as a linear function of the number of pieces of jewelry, x?

Answer 1

Slope:

m = ( y2 - y1 )/(x2 - x1)

m = ( 11200 - 6400 )/(20 - 10)

m = ( 4800 )/(10)

m = 480


So the slope is m = 480


Now use y = mx+b and then plug in m = 480, x = 10 and y = 6400


y = mx+b

y = 480x + b

6400 = 480(10) + b

6400 = 4800 + b

6400 - 4800 = b

1600 = b

b = 1600


So the equation is y = 480x+1600 which is also C(x) = 480x+1600

Answer 2

thanks you jim :D

Answer 3

You can check the answer

If x = 10, then...

C(x) = 480x+1600

C(10) = 480(10)+1600

C(10) = 4800+1600

C(10) = 6400

So that works

-----------------------

If x = 20, then...

C(x) = 480x+1600

C(10) = 480(20)+1600

C(10) = 9600+1600

C(10) = 11200

So that works as well

Answer 4

yw