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

Explanation:

Step1: Recall line - of - best - fit concept

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use a graphing calculator or estimate by looking at the trend of the data. As the font size ($x$) increases, the word count ($y$) decreases, so the slope $m$ should be negative.

Step2: Estimate using two points

Let's take two points from the data, say $(10,407)$ and $(24,138)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{138 - 407}{24 - 10}=\frac{- 269}{14}\approx - 19.2$. But a more accurate way is to use a calculator's linear regression function. However, we can also test the given equations by substituting some $x$ values from the data. Let's take $x = 14$. For $y=-55x + 407$, when $x = 14$, $y=-55\times14 + 407=-770+407=-363$ (way off). For $y=-41x + 814$, when $x = 14$, $y=-41\times14 + 814=-574 + 814 = 240$ (not close). For $y=-38x + 922$, when $x = 14$, $y=-38\times14+922=-532 + 922=390$ (relatively close). For $y=-26x + 723$, when $x = 14$, $y=-26\times14 + 723=-364+723 = 359$ (also close). Let's take another value, say $x = 16$. For $y=-38x + 922$, when $x = 16$, $y=-38\times16+922=-608 + 922 = 314$. For $y=-26x + 723$, when $x = 16$, $y=-26\times16+723=-416+723 = 307$. The actual value for $x = 16$ is $280$ (from the table). The equation $y=-38x + 922$ gives a closer approximation overall.

Answer:

$y=-38x + 922$