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?

Answer 1

Answer:

$m=25g$  direct variation

Step-by-step 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

$\frac{125}{5}\frac{miles}{gallons}=25\frac{miles}{gallons}$

$\frac{175}{7}\frac{miles}{gallons}=25\frac{miles}{gallons}$

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

$\frac{m}{g}=k$  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

$k=25\frac{miles}{gallons}$

substitute

$m=kg$ -------> $m=25g$

Answer 2

First find out how much in that one week, the amount of miles per gallon

125/5 = 25, or 25 mpg

Find out how much for the next week

175/7 = 25, or 25 mpg

Note: 
g = gallons
m = miles

you're equation will be:
m = 25(g)

For every gallon (g), you multiply it by 25 to get miles (m).


hope this helps