Question

jamal 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?

Explanation:

Step1: Recall the concept of slope in a linear relationship

The slope \(m\) of a line \(y = mx + b\) is given by the formula \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is the change in the \(y -\)variable and \(\Delta x\) is the change in the \(x -\)variable.

Step2: Identify the variables in the context

In this problem, the \(y -\)variable is the catfish weight (in pounds) and the \(x -\)variable is the catfish length (in inches).

Step3: Interpret the slope

The slope \(\frac{\Delta y}{\Delta x}=\frac{\text{Change in weight}}{\text{Change in length}}\). So, the slope represents the change in weight (in pounds) per unit change in length (in inches).

Answer:

The slope represents the change in the weight of the catfish (in pounds) per one - inch change in the length of the catfish.