Question

Identify as a direct variation, inverse variation or neither. Is the total cost to fill a car gas tank a direct or inverse variation with respect to the number of gallons used?

Answer 1

It's a direct because you're paying to refill the gallons of gas used.

Answer 2

It is a case of a direct variation.

Explanation:

Direct variation--

Two variables x and y are said to be in direct variation if there exist a constant k such that:

`y=kx`

i.e. with the increase/decrease in one variable the other variable also increases/decreases.

Inverse variation--

Two variables x and y are said to be in inverse variation if there exist a constant k such that:

`xy=k`

i.e. with the increase in one variable the other decreases and vice-versa.

Here the independent variable is: Number of gallons used.

and the dependent variable is: Total cost to fill a car gas tank.

As we know that as the number of gallons used increases the total cost also increases and it increases by some constant k.

Since, the cost of per gallons is some fixed.