Question

One week, Kerry travels 125 miles and uses 5 gallons of gasoline. The next week, she travels 175 miles and uses 7 gallons of gasoline. Which best describes the function that can be used to represent m, the number of miles traveled, and g, the number of gallons used? direct variation; m = kg direct variation; gm = k inverse variation; inverse variation;

Answer 1

m = kg

Explanation:

125 = 5k , k = 25 where k is the constant of variation.

175 = 7k, k = 25

Direct variation m = kg

Answer 2

`m=kg` direct variation

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In this problem

Let

m------> the number of miles traveled

g------> the number of gallons used

we have that

`(125)/(5)(miles)/(gallons)=25(miles)/(gallons)`

`(175)/(7)(miles)/(gallons)=25(miles)/(gallons)`

The linear direct variation that represent the situation is equal to the equation

`(m)/(g)=k` or
`m=kg`

where

k is the constant of proportionality

In a direct variation the constant k is equal to the slope m of the line, and the line passes through the origin

`k=25(miles)/(gallons)`

substitute

`m=kg` ------->
`m=25g`