Question

jocelyn decides to research the relationship between the length in inches and the weight of a certain species of catfish. she measures the length and weight of a number of specimens she catches, then throws back into the water. after plotting all her data, she draws a line of best fit. based on the line of best fit, how much would you predict a catfish with a length of 32 inches would weigh? answer attempt 1 out of 2 pounds submit answer

Explanation:

Step1: Find the slope of the line of best fit

Use the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(20,4)\) and \((x_2,y_2)=(23,10)\).
\(m=\frac{10 - 4}{23 - 20}=\frac{6}{3}=2\)

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using \((x_1,y_1)=(20,4)\) and \(m = 2\), we get \(y-4=2(x - 20)\).
Expand: \(y-4=2x-40\), so \(y = 2x-36\)

Step3: Predict the weight for \(x = 32\)

Substitute \(x = 32\) into the equation \(y=2x - 36\).
\(y=2\times32-36\)
\(y = 64-36\)
\(y = 28\)

Answer:

\(28\)