A graph of the cost of gas purchased depending on the number of gallons pumped has the points (4,15) and (8,30). What is the rate of change in the cost of gas as each gallon is pumped?

Answer 1

To find the rate of change in the cost of gas with respect to the number of gallons pumped, we can use the two points given: (4, 15) and (8, 30).

The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

In this case:

• \((x_1, y_1) = (4, 15)\)
• \((x_2, y_2) = (8, 30)\)

Substituting these values into the formula gives us:

\[ \text{slope} = \frac{30 - 15}{8 - 4} = \frac{15}{4} \]

Thus, the rate of change in the cost of gas as each gallon is pumped is \( \frac{15}{4} \) dollars per gallon, or \( 3.75 \) dollars per gallon.