Final answer:
To find the number of soda bottles the machine can make each minute, calculate the slope of the line that passes through the points (2,72) and (5,180). The slope is 36, which represents the production rate of 36 bottles per minute.
Step-by-step explanation:
The student is asking how to find the rate at which a machine produces soda bottles per minute using two given points on a graph. To find this rate, you need to calculate the slope of the line that passes through the points (2,72) and (5,180). The slope can be found using the formula:
slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Substituting the given points:
m = (180 - 72) / (5 - 2) = 108 / 3 = 36
The slope of the line is 36 bottles per minute, which is the number of soda bottles the machine can produce each minute.