The price of buying gasoline varies directly with the number of gallons bought. If 12 gallons of gas cost $32.64, what is the rate of change of this linear function?

Answer 1

Hi Maiali,

For direct variation, the rate of change will be equal to the unit rate (or the cost of 1 gallon of gas).

You can determine the unit rate using the information given in your problem:

$32.62 = x

12 gallons 1 gallon

Divide the numerator and denominator by 12:

$32.62 ÷ 12 = $2.72

12 gallons ÷ 12 1 gallon

The rate of change will be: $2.72

1 gallon

Answer 2

given information rate of gas varies with the amount bought in a direct proportion.

that means less gallons cost less and more gallons cost more

12 gallons cost = 32.64 dollars

find the rate of change of this linear function

the rate of change of linear function denoted by k is nothing but y/x ( corresponding y / corresponding x ) on a straing line of linear equation. ( when the rate of change is directly proportional the line passes through the origin). we can also call it as a unit rate as it is constant for every pair of co ordinates. can say it as slope too!

so here it is k = 32.64/12

= k= 2.72

so the rate of change here is 2.72.

that means the cost of 1 gallon or 1 unit of gallon = $2.72.