rob is investigating the effects of font size on the number of words that fit on a page. he changes the font…

Answer:

B. $y = - 41x+814$

Explanation:

Step1: Recall line - of - best - fit concept

The line of best fit is of the form $y = mx + b$ where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze slope trend

As font size ($x$) increases, the number of words per page ($y$) decreases, so the slope $m$ should be negative.

Step3: Use a point - slope approximation

We can take two points, say $(10,407)$ and $(14,352)$. The slope $m=\frac{352 - 407}{14 - 10}=\frac{- 55}{4}=-13.75$ (a rough estimate). A more accurate way is to use a graphing utility or statistical software to calculate the least - squares regression line. But we can also test the given equations by substituting some $x$ values from the data. Let's take $x = 12$. For $y=-55x + 407$, when $x = 12$, $y=-55\times12 + 407=-660+407=-253$ (way off). For $y=-41x + 814$, when $x = 12$, $y=-41\times12 + 814=-492+814 = 322$. For $y=-38x + 922$, when $x = 12$, $y=-38\times12+922=-456 + 922=466$. For $y=-26x + 723$, when $x = 12$, $y=-26\times12+723=-312+723 = 411$. Looking at the data point for $x = 12$, the word count is $435$ and $y=-41x + 814$ gives a value closest to the actual data among the options when we do these simple substitutions.