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

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

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((30,27)\) and \(m = 2\), we have \(y-27=2(x - 30)\).
Expand it: \(y-27=2x-60\). Then \(y=2x - 33\)

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

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

Answer:

\(33\) pounds