Question

question
carter 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?
answer attempt 1 out of 2
inches

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