Question

kayden 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. based on the line of best fit, how much would you predict a catfish with a length of 33 inches would weigh?

Explanation:

Step1: Find the slope of the line

We use two points on the line of best fit \((x_1,y_1)=(30,27)\) and \((x_2,y_2)=(31,29)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute the values: \(m=\frac{29 - 27}{31 - 30}=\frac{2}{1}=2\).

Step2: Use the point - slope form to find the equation of the line

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((30,27)\) and \(m = 2\), we have \(y-27=2(x - 30)\).
Expand: \(y-27=2x-60\).
Solve for \(y\): \(y=2x - 33\).

Step3: Predict the weight when \(x = 33\)

Substitute \(x = 33\) into the equation \(y=2x-33\).
\(y=2\times33-33\).
\(y = 66-33\).
\(y = 33\).

Answer:

33