express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a

Question

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi.

Answer 1

Note: "Linear" means straight-line. So we can plot a straight line graph to find the relationship.
Let d = # of miles driven
Let C = cost

So we have:
480 miles = $380
800 miles = $460

Then the points on a graph are: (480,380) and (800,460).

Find the equation of a line passing through these points and you're done.
Gradient = (C2-C1) / (d2-d1)
= (460-380) / (800-480)
= 80/320
= 0.25

So the equation of a line is:
C-C1 = m(d-d1), where m is the gradient and (d1,C1) is a point.
Let's use: (480,380) as the point (d1,C1)
Then the equation of the line is:
C - 380 = 0.25(d-480)
C - 380 = 0.25d - 120
Add 380 to both sides:

C = 0.25d + 260

The equation of the line is the same as the linear relationship. Therefore our final answer is:

C = 0.25d + 260

Answer 2

If it is a linear function then
Cost, c = kd + p, where d = distance, k ,p are constants

Eqn 1: 380 = 480k + p, for May
Eqn 2: 460 = 800k + p, for June

Eqn 2 - Eqn1:
80 = 320k
k = 1/4

Now put k=1/4 into 1
380 = 480/4 + p
p = 380 - 120 = 260

hence, c = d/4 + 260

Answer 3

For 480 miles we have 380$
For 800 miles we have 460$

We can subtract the two giving:
For each additional:
320 miles - 80$
160 miles - 40$
480 miles - 120$

Subtract this from the first item:
0 miles - 260$

C = md + 260 (m is gradient)
m = 40 / 160
m = 1 / 4
m = 0.25

C = 0.25d + 260

Answer 4

C = ($460 - $380)(d - 480)/(800 - 480) + $380