ian decides to research the relationship between the length in inches and the weight of a certain species of…

Explanation:

Step1: Find two points on the line of best - fit

We can use the points $(30,25)$ and $(31,27)$ from the line of best - fit.

Step2: Calculate the slope of the line

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(30,25)$ and $(x_2,y_2)=(31,27)$. Then $m=\frac{27 - 25}{31 - 30}=\frac{2}{1}=2$.

Step3: Use the point - slope form of a line

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(30,25)$ and $m = 2$, we have $y-25=2(x - 30)$.

Step4: Rewrite in slope - intercept form

$y-25=2x-60$, so $y = 2x-35$.

Step5: Substitute $y = 29$ (weight) to find $x$ (length)

Set $y = 29$ in $y = 2x-35$. Then $29=2x-35$.

Step6: Solve for $x$

Add 35 to both sides: $29 + 35=2x$, so $64 = 2x$. Divide both sides by 2: $x = 32$.

Answer:

32 inches