which situation is most likely to have a constant rate of change?\na. points scored in a basketball game…

Explanation:

Step1: Analyze option A

In a basketball game, the points scored per quarter can vary greatly. For example, a team might score 20 points in the first quarter, 15 in the second, 30 in the third, etc. So, the rate of change (points per quarter) is not constant.

Step2: Analyze option B

The distance a delivery truck travels depends on many factors like the location of each delivery. The distance per delivery is not likely to be the same. For instance, one delivery could be 5 miles away and another 15 miles away. So, the rate of change (distance per delivery) is not constant.

Step3: Analyze option C

The price of gas is usually a fixed amount per gallon (say (p) dollars per gallon). If (y) is the total amount paid and (x) is the number of gallons purchased, then the relationship is (y = px). The rate of change (the slope (p)) is constant. For example, if gas is ($3) per gallon, for 1 gallon (y = 3\times1=$3), for 2 gallons (y=3\times 2 = $6), and the rate of change (change in (y) over change in (x)) is (\frac{6 - 3}{2-1}=3).

Step4: Analyze option D

The number of flowers in a flower - bed compared to the area planted can vary. Different types of flowers have different densities. For example, one type of flower might have 10 flowers per square foot and another type 5 flowers per square foot. So, the rate of change (number of flowers per square foot) is not constant.

Answer:

C. The total amount paid for gas compared with the number of gallons purchased.