A biologist studied the number of catfish in a small lake during an 8-month period. The line graphed on the coordinate grid shows the relationship between the number of months of the study and the number of catfish in the lake. What is the meaning of the rate of change for the line in the graph? A. It means the number of catfish increased at a rate of 4 catfish per month. B. It means the number of catfish increased at a rate of 30 catfish per month. C. It means the initial number of catfish was 4. D.I means the initial number of catfish was 30.

Question

A biologist studied the number of catfish in a small lake during an 8-month period. The line graphed on the coordinate grid shows the relationship between the number of months of the study and the number of catfish in the lake. What is the meaning of the rate of change for the line in the graph? A. It means the number of catfish increased at a rate of 4 catfish per month. B. It means the number of catfish increased at a rate of 30 catfish per month. C. It means the initial number of catfish was 4. D.I means the initial number of catfish was 30.

Answer 1

To determine the meaning of the rate of change for the line in the graph, we need to calculate the slope of the line. The slope represents the rate of change and is calculated by the change in the y-values (number of catfish) divided by the change in the x-values (number of months).Given the two points on the line (0,30) and (8,62), we can calculate the slope as follows:Step 1: Identify the coordinates of the two points.Point 1: (x1, y1) = (0, 30)Point 2: (x2, y2) = (8, 62)Step 2: Use the slope formula:slope (m) = (y2 - y1) / (x2 - x1)Step 3: Substitute the values into the formula:m = (62 - 30) / (8 - 0)m = 32 / 8m = 4The slope of the line is 4, which means the rate of change is 4 catfish per month. This represents the average increase in the number of catfish each month over the 8-month period.Answer:A. It means the number of catfish increased at a rate of 4 catfish per month.

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