Question

pedro 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, what would you predict to be the length of a catfish that weighed 49 pounds?

Explanation:

Step1: Find the slope of the line of best fit

Use the two - point formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(20,13)\) and \((x_2,y_2)=(24,22)\).
\(m=\frac{22 - 13}{24 - 20}=\frac{9}{4}=2.25\)

Step2: Find the equation of the line of best fit

Use the point - slope form \(y - y_1=m(x - x_1)\). Using \((x_1,y_1)=(20,13)\) and \(m = 2.25\), we have \(y-13=2.25(x - 20)\).
Expand: \(y-13=2.25x-45\). Then \(y = 2.25x- 32\)

Step3: Predict the length when the weight \(y = 49\)

Substitute \(y = 49\) into the equation \(49=2.25x-32\).
Add 32 to both sides: \(49 + 32=2.25x\), so \(81=2.25x\).
Divide both sides by \(2.25\): \(x=\frac{81}{2.25}=36\)

Answer:

The predicted length of the catfish is 36 inches.