Question

question
jocelyn 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?
answer attempt 1 out of 2
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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