Question

jin 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 \((30,24)\) and \((31,26)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{26 - 24}{31 - 30}=\frac{2}{1}=2\)

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

Using the point - slope form \(y - y_1=m(x - x_1)\), with \(m = 2\) and the point \((30,24)\)
\(y-24=2(x - 30)\)
\(y-24=2x-60\)
\(y=2x - 36\)

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

Substitute \(x = 33\) into the equation \(y=2x - 36\)
\(y=2\times33-36\)
\(y = 66-36\)
\(y = 30\)

Answer:

\(30\)