question\ncarter decides to research the relationship between the length in inches and the weight of a…
question\ncarter 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, what would you predict to be the length of a catfish that weighed 60 pounds?\nanswer attempt 1 out of 2\ninches
Answer
Explanation:
Step1: Find the slope of the line
The line passes through points $(20,15)$ and $(28,33)$. The slope $m$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{33 - 15}{28 - 20}=\frac{18}{8}=\frac{9}{4}$.
Step2: Find the equation of the line
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(20,15)$ and $m = \frac{9}{4}$, we have $y-15=\frac{9}{4}(x - 20)$. Expanding gives $y-15=\frac{9}{4}x-45$, and then $y=\frac{9}{4}x - 30$.
Step3: Solve for $x$ when $y = 60$
Substitute $y = 60$ into the equation $y=\frac{9}{4}x - 30$. So, $60=\frac{9}{4}x-30$. Add 30 to both sides: $60 + 30=\frac{9}{4}x$, which is $90=\frac{9}{4}x$. Multiply both sides by $\frac{4}{9}$ to solve for $x$. We get $x = 40$.
Answer:
40