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 the gas as each gallon is pumped?
To find the rate of change in the cost of gas per gallon, we need to calculate the slope of the line connecting the two given points. Recall that the slope of a line is found by dividing the change in y-values by the change in x-values:
slope = (change in y) / (change in x)
Using the two given points, we get:
change in y = 30 - 15 = 15
change in x = 8 - 4 = 4
So the slope is:
slope = 15 / 4 = 3.75
Therefore, the rate of change in the cost of gas per gallon is $3.75. For every additional gallon of gas pumped, the cost increases by $3.75.