Question

rob is investigating the effects of font size on the number of words that fit on a page. he changes the font size on an essay and records the number of words on one - page of the essay. the table shows his data. words per page font size 14 12 16 10 12 14 16 18 24 22 word count 352 461 340 407 435 381 280 201 138 114 which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page? o y=-55x + 407 o y=-41x + 814 o y=-38x + 922 o y=-26x + 723

Explanation:

Step1: Recall line - of - best - fit formula

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 software to find the line of best fit. Another way is to use the general trend of the data. As the font size ($x$) increases, the number of words per page ($y$) decreases, so the slope $m$ is negative.

Step2: Estimate slope and y - intercept

We can take two points from the data (for simplicity, we can take the first and the last points: $(14,352)$ and $(22,114)$). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
$m=\frac{114 - 352}{22 - 14}=\frac{-238}{8}=-29.75\approx - 30$.
We can also use the point - slope form $y - y_1=m(x - x_1)$ with the point $(14,352)$ and $m\approx - 30$.
$y-352=-30(x - 14)$
$y-352=-30x + 420$
$y=-30x+772$.
Let's check the given options. Option C: $y=-38x + 922$. If we substitute some values of $x$ from the data set and compare with the actual $y$ values, we can see that it is a reasonable fit.

Answer:

$y=-38x + 922$