Question

1. the table below shows the lengths (in inches) and corresponding weights (in pounds) of sand sharks. predict the weight of a sand shark whose length is 75 inches. type a response

Explanation:

Step1: Calculate the slope

Let \(x\) be the length and \(y\) be the weight.
We take two points \((x_1,y_1)=(60,105)\) and \((x_2,y_2)=(72,158)\)
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{158 - 105}{72 - 60}=\frac{53}{12}\approx4.42\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((60,105)\) and \(m = \frac{53}{12}\)
\(y-105=\frac{53}{12}(x - 60)\)
\(y-105=\frac{53}{12}x-265\)
\(y=\frac{53}{12}x-265 + 105\)
\(y=\frac{53}{12}x-160\)

Step3: Predict for \(x = 75\)

Substitute \(x = 75\) into \(y=\frac{53}{12}x-160\)
\(y=\frac{53\times75}{12}-160\)
\(y=\frac{3975}{12}-160\)
\(y = 331.25-160\)
\(y=171.25\)

Answer:

\(171.25\) pounds