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 the fact that as the font size ($x$) increases, the word count ($y$) decreases, so the slope $m$ should be negative.

Step2: Use a point - testing method

Let's take a point from the data, say $(x = 14,y = 352)$.
For $y=-55x + 407$, when $x = 14$, $y=-55\times14 + 407=-770+407=-363$ (not close).
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).
We can also consider the general trend. As the font - size increases, the decrease in word - count should be relatively steep.
The slope of $y=-38x + 922$ gives a better approximation of the rate of change in the data.

Answer:

$y=-38x + 922$