Step 1 :Given two points (3,132) and (8,352), we need to find the slope of the line passing through these points.
Step 2 :The formula for the slope of a line given two points (x1, y1) and (x2, y2) is: \(\text{Slope} = \frac{y2 - y1}{x2 - x1}\)
Step 3 :Substituting the given points into the formula, we get: \(\text{Slope} = \frac{352 - 132}{8 - 3} = \frac{220}{5}\)
Step 4 :\(\text{Slope} = 44\)
Step 5 :Therefore, the machine can make 44 soda bottles per minute. So, the final answer is \(\boxed{44}\)