Question

question
laraughn 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 32 pounds?

Explanation:

Step1: Identify two points on the line of best fit

From the graph, we can see two points on the line of best fit: \((30, 26)\) and \((34, 22)\) (assuming the coordinates are \((weight, length)\)).

Step2: Calculate the slope of the line

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{22 - 26}{34 - 30}=\frac{- 4}{4}=- 1\).

Step3: Use the point - slope form to find the equation of the line

The point - slope form is \(y - y_1=m(x - x_1)\). Let's use the point \((30, 26)\).
\(y - 26=-1(x - 30)\)
Simplify the equation: \(y-26=-x + 30\), so \(y=-x + 56\), where \(y\) is the length (inches) and \(x\) is the weight (pounds).

Step4: Predict the length for a weight of 32 pounds

Substitute \(x = 32\) into the equation \(y=-x + 56\).
\(y=-32 + 56=24\).

Answer:

The predicted length of the catfish that weighs 32 pounds is 24 inches.