Question

michael 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 33 pounds?

Explanation:

Step1: Identify two points on the line

We can take two points on the best - fit line, say $(20,5)$ and $(30,25)$.

Step2: Find the slope of the line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(20,5)$ and $(x_2,y_2)=(30,25)$. Then $m=\frac{25 - 5}{30 - 20}=\frac{20}{10}=2$.

Step3: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(20,5)$ and $m = 2$, we have $y - 5=2(x - 20)$. Expanding gives $y-5 = 2x-40$, so $y=2x - 35$.

Step4: Predict the length when weight is 33 pounds

We want to find $x$ when $y = 33$. Substitute $y = 33$ into the equation $33=2x-35$.

Step5: Solve for x

Add 35 to both sides: $33 + 35=2x$, so $68 = 2x$. Divide both sides by 2: $x = 34$.

Answer:

34