As Evin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of driving, it has 3.5 gallons of gas left in it. The rate at which she is LOSING gas is 1.25 gallons....So, the slope is -1.25. How many gallons did she have to START?

The slope in this scenario is -1.25 gallons per mile, this means that for every mile that Evin drives she is wasting 1.25 gallons of gasoline. Since she only drove 1 hour at the begining and after that hour her tank had 7.25 gallons, then we can simply add 1.25 gallons to her tank at this moment to make up for the 1 hour she drove and that would give us the total amount of gas she had before she started driving.

7.25 + 1.25 = 8.50 gallons of gas.

raphealnwobi raphealnwobi · Answer 2 · 2021-12-03T12:12:17+01:00

Evin was losing gas at a rate of 1.25 gallons per hour and she started with 8.5 gallons.

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let y represent the amount of gallons left after x hours.

She notices that after 1 hour her gas tank has 7.25 gallons left. Hence:

7.25 = m(1) + b

m + b = 7.25 (1)

After 4 hours of driving, it has 3.5 gallons of gas left in it. Hence:

3.5 = 4(m) + b

4m + b = 3.5 (2)

Solving equations 1 and 2 simultaneously gives m = -1.25, b = 8.5

Hence Evin was losing gas at a rate of 1.25 gallons per hour and she started with 8.5 gallons.

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