Question

question sebastian 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, how much would you predict a catfish with a length of 45 inches would weigh?

Explanation:

Step1: Find the slope of the line

The line passes through points $(20,5)$ and $(30,23)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{23 - 5}{30 - 20}=\frac{18}{10} = 1.8$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(20,5)$. Substitute $m = 1.8$, $x_1=20$ and $y_1 = 5$ into $y - y_1=m(x - x_1)$ gives $y-5=1.8(x - 20)$. Expand to get $y-5=1.8x-36$. Then $y=1.8x - 31$.

Step3: Make a prediction

We want to find the weight $y$ when $x = 45$. Substitute $x = 45$ into $y=1.8x - 31$. So $y=1.8\times45-31=81 - 31=50$.

Answer:

50