find a linear function given an odometer reading, time, and the fuel tank reading.

Question

when David Arnold started out on his trip his odometer read 45973 and his fuel gauge read 7/8 full. Exactly 1hr and 48 min later his the odometer read 46081 and the fuel gauge read 1/2 full. Find an equation for the linear function of the fuel gauge reading

 

Assume that this would be linear. I am having trouble figuring out what is needed of me and how to do what I need to do. I appreciate any help you can offer. -Adi 

Answer 1

45973 was initial mileage

46081 was final mileage

 

distance travelled was 108 miles

 

fuel per miles...

Relating fuel as a function of miles driven we have two points:

Letting x = # miles driven

and y = amount of fuel left

Having driven zero miles we had 7/8 of a tank... (0, 7/8)

Having driven 108 miles we had 1/2 of a tank... (108, 1/2)

 

Find the slope:  m = (1/2 - 7/8)/(108-0) = (-3/8)/108 = -1/288

 

y = (-1/288)x + b

 

b is the y-intercept which we already have.. b = 7/8

 

y = (-1/288)x + 7/8

 

If you wish to get rid of the fractions, multiply through by 288 to get:

 

288y = -x + 252