question\njocelyn decides to research the relationship between the length in inches and the weight of a…
question\njocelyn decides to research the relationship between the length in inches and the weight of a certain species of catfish. she measures the length and weight of a number of specimens she catches, then throws back into the water. after plotting all her data, she draws a line of best fit. based on the line of best fit, how much would you predict a catfish with a length of 32 inches would weigh?\nanswer attempt 1 out of 2\npounds submit answer
Answer
Explanation:
Step1: Find the slope of the line
The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(20,4)$ and $(29,22)$. Then $m=\frac{22 - 4}{29 - 20}=\frac{18}{9}=2$.
Step2: Find the y - intercept
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(20,4)$ and $m = 2$, we have $y-4=2(x - 20)$. Expanding gives $y-4=2x-40$, so $y=2x - 36$.
Step3: Predict the weight
We want to find the weight when $x = 32$. Substitute $x = 32$ into the equation $y=2x - 36$. Then $y=2\times32-36=64 - 36=28$.
Answer:
28