A data plan is linear function of 6 GB for $65/mth and 9 GB plan for $85/mth. What is function C (x) where C is mthly cost of plan in and x of GB of data.

Question

How do I set it up to find the cost of linear function c(x)?  Am I missing something?

Answer 1

The easiest way to solve this is to think of the 6 GB for $65 and the 9 GB for $85 as linear points as (x, C).

 

The points then become: (6,65) and (9,85).

 

To find the slope of the function (m) remember the equation m=(ΔC/Δx)

 

m= (85-65)/(9-6)= 20/3

 

From the slope and knowing it's a linear function we can use the slope-intercept form: C(x)= mx+b and plug in one of the points:

 

65= 6*(20/3)+b

65=40+b

25=b

 

The equation we get is C(x)= (20/3)x + 25, but let's double check with the other point:

 

C(9)= (20/3)*9 +25

C(9)= 60+25=85

 

Since it came out with the right value we know that function is C(x)= (20/3) + 25