question sebastian decides to research the relationship between the length in inches and the weight of a…
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?
Answer
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