On a cross-country trip, a car uses 5 gallons of gas for every 120 miles it travels. How many gallons of gas does the car use if it travels 600 miles? How far can the car travel if it uses 30 gallons of gas?
Make a table of equivalent ratios to help you answer the questions. Then graph the ratios.
a
The car uses gallons of gas if it travels 600 miles.

Step-by-step explanation:

120 miles / 5 gallons of gas = 24 miles per gallon

1. How many gallons of  gas does the car use if it travels 600 miles?

Equation: 600=24x     (600 representing miles, 24 miles per gallon)

                600=24x

                 24    24     (cancel out 24 from the right side of equation)

                 x = 25 gallons

2.  How far can the car travel if it uses 30 gallons of gas?

30 gallons x 24 miles per gallon = 720 miles

3. Ratios:

0 gallons : 0 miles  (0,0)

1 gallons : 24 miles  (1,24)

2 gallons : 48 miles  (2,48)

So on so forth...

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: