Question

based on the line of best fit, what would you predict to be the length of a catfish that weighed 49 pounds? catfish weight (pounds) catfish length (inches) (20,13) (24,22) (28,31)

Explanation:

Step1: Find the slope of the line of best fit

We have two points on the line of best fit: \((20, 13)\) and \((24, 22)\) and \((28, 31)\). Let's use \((20, 13)\) and \((28, 31)\) to calculate the slope \(m\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 20,y_1 = 13,x_2=28,y_2 = 31\), we get \(m=\frac{31 - 13}{28 - 20}=\frac{18}{8}=\frac{9}{4}=2.25\)

Step2: Find the equation of the line of best fit

Using the point - slope form \(y - y_1=m(x - x_1)\), we use the point \((20,13)\) and \(m = \frac{9}{4}\).
\(y-13=\frac{9}{4}(x - 20)\)
\(y-13=\frac{9}{4}x-45\)
\(y=\frac{9}{4}x-45 + 13\)
\(y=\frac{9}{4}x-32\)

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

We substitute \(y = 49\) into the equation \(y=\frac{9}{4}x-32\)
\(49=\frac{9}{4}x-32\)
Add 32 to both sides: \(49 + 32=\frac{9}{4}x\)
\(81=\frac{9}{4}x\)
Multiply both sides by \(\frac{4}{9}\): \(x=\frac{81\times4}{9}\)
\(x = 36\)

Answer:

The predicted length of the catfish that weighs 49 pounds is 36 inches.