Question

khalil decides to research the relationship between the length in inches and the weight of a certain species of catfish. he measures the length and weight of a number of specimens he catches then throws back into the water. after plotting all his data, he draws a line of best fit. what does the slope of the line represent? answer the expected weight of a catfish that is 1 inch long. the expected length of a catfish that weighs 1 pound. the expected change in weight of a catfish for each additional inch in length. the rate of change in the expected length of the catfish over its weight.

Explanation:

The slope of a line in a linear relationship \(y = mx + b\) (where \(y\) is the dependent variable and \(x\) is the independent variable) represents the rate of change of \(y\) with respect to \(x\). In this context, the \(y\) - axis is catfish weight (pounds) and the \(x\) - axis is catfish length (inches). So, the slope \(m=\frac{\Delta y}{\Delta x}\), which means for a unit change in \(x\) (one additional inch in length), we get the change in \(y\) (weight).

Answer:

The expected change in weight of a catfish for each additional inch in length.