Question

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? answer the expected weight of a catfish that is 1 inch long. the expected length of a catfish that weighs 1 pound. the rate of change in the expected length of the catfish over its weight. the rate of change in the expected weight of the catfish over its length.

Explanation:

Step1: Recall slope concept

The slope of a line in a linear - relationship $y = mx + b$ is given by $m=\frac{\Delta y}{\Delta x}$. In the context of the catfish data, let $x$ be the length of the catfish (in inches) and $y$ be the weight of the catfish (in pounds).

Step2: Interpret $\Delta y$ and $\Delta x$

The change in $y$ ($\Delta y$) represents the change in weight, and the change in $x$ ($\Delta x$) represents the change in length. So, the slope $m = \frac{\Delta y}{\Delta x}$ is the rate of change of the weight ($y$ - variable) with respect to the length ($x$ - variable).

Answer:

The rate of change in the expected weight of the catfish over its length.