Question

Fantastic Furniture builds sofas. It costs $2,725 to build 9 sofas and $3,850 to build 14 sofas.

Which equation represents the cost, C(x), as a linear function of the number of sofas, x?

Answer 1

a. C(x) = 225x - 700

b. C(x) = 225x + 700

c. C(x) = 700x - 225

d. C(x) = 700x + 225

Answer 2

We have two points on our line: (9, 2725) and (14, 3850).

Using point-slope form:
\[ \Large m = {(y_1 – y_0) \over (x_1 – x_0)} \\ \ \\ \Large m = {(3850 – 2725) \over (14 – 9)} \]
So, \(m = 245\).

Pluggin' it in to our slope intercept form:
y = C(x) = mx + b
= 245x + b

So next up, we find b by plugging in the values for x and y from any point we choose. Let's choose (9, 2725):

y = 245x + b
(2925) = 245(9) + b
b = 720

Pluggin' that back into our equation:
y = C(x) = mx + b
= 245x + b
= 245x + 720

C(x) = 245x + 720

Answer 3

But that's not an option ...

Answer 4

Whoops, I messed up on my calculation for m.

m=225.

I'll leave the rest up to you to figure out.

Answer 5

you need the line through the points \((9, 2725)\) and \((14,3580)\)
calculation is annoying, just ask
http://www.wolframalpha.com/input/?i=line+%289%2C2725%29%2C%2814%2C3850%29

looks like the answer is B