Question

The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4000 to produce 300 chairs in one day.
(a) Assuming that the relationship between cost C and the number of chairs produced x is linear, find an equation that expresses this relationship.

Answer 1

You have two points (100,2200) and (300,4000)

Find the equation of the line that goes through these points. Let me know if you need help doing that.

Answer 2

i got y=9x-2600

Answer 3

The slope is 9, but the y-intercept is NOT -2600

Answer 4

y = mx+b

y = 9x + b

2200 = 9(100) + b

2200 = 900 + b

Keep going to solve for b

Answer 5

b=1300 but i dont understand how you got that equation

Answer 6

y = mx+b

y = 9x + b ... Plug in m = 9 (the slope you found earlier)

2200 = 9(100) + b ... Plug in (100, 2200) or x = 100 and y = 2200

....

Answer 7

i see what i did wrong for some reason i used 100 and 300 instead of 2200 and 100

Answer 8

Yes use the corresponding x (number) and y (cost) values

Answer 9

x = 100 doesn't correspond to y = 300, but x = 100 corresponds to y = 2200

Answer 10

i was still partially thinking slope instead of point-slope form

Answer 11

i see

Answer 12

the second and third parts of my question ask what my slope and y-int is and what they represent. I know what my slope and y-int is just not what they represent

Answer 13

slope represents the change in cost over the change in number of chairs made

Answer 14

so it's the cost per chair

Answer 15

so it costs $9 a chair

Notice how as x gets bigger by one, y will get bigger by 9 (because of the slope)

Answer 16

The y-intercept is the starting cost to do business regardless of how many chairs are made (think of this as the cost of rent, electricity, etc etc)

Answer 17

So it costs $1300 to keep the lights on and the machines running (no matter if 0 chairs or 100 chairs are made)

Answer 18

Thank your so much for helping me!

Answer 19

yw