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? y = -55x + 407 y = -41x + 814 y = -38x + 922 y = -26x + 723

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 point - slope approach 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 $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{138 - 407}{24 - 10}=\frac{- 269}{14}\approx - 19.21$. But a quicker way is to check each option by substituting some $x$ values from the data.
For option 1: When $x = 10$, $y=-55\times10 + 407=-550+407=-143$ (way off).
For option 2: When $x = 10$, $y=-41\times10 + 814=-410 + 814 = 404$. When $x = 24$, $y=-41\times24+814=-984 + 814=-170$ (not a good fit).
For option 3: When $x = 10$, $y=-38\times10 + 922=-380+922 = 542$ (off).
For option 4: When $x = 10$, $y=-26\times10+723=-260 + 723 = 463$. When $x = 24$, $y=-26\times24+723=-624+723 = 99$. This option seems to fit the general trend of the data better than the others.

Answer:

$y=-26x + 723$