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
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: Check each equation with sample data points

Take \(x = 10\) (font size) and check \(y\) (word count = 407)
- For \(y=-55x + 407\): \(y=-55\times10+407=-550 + 407=-143\) (incorrect)
- For \(y=-41x + 814\): \(y=-41\times10+814=-410+814 = 404\) (close)
- For \(y=-38x + 922\): \(y=-38\times10+922=-380+922=542\) (incorrect)
- For \(y=-26x + 723\): \(y=-26\times10+723=-260+723 = 463\) (incorrect)

Take \(x = 12\) (font size) and check \(y\) (word count = 461 or 435)
- For \(y=-41x + 814\): \(y=-41\times12+814=-492+814 = 322\) (incorrect)
Take \(x = 14\) (font size) and check \(y\) (word count = 352 or 381)
- For \(y=-41x + 814\): \(y=-41\times14+814=-574+814=240\) (incorrect)
Take \(x = 16\) (font size) and check \(y\) (word count = 340 or 280)
- For \(y=-41x + 814\): \(y=-41\times16+814=-656+814 = 158\) (incorrect)
Take \(x = 18\) (font size) and check \(y\) (word count = 201)
- For \(y=-41x + 814\): \(y=-41\times18+814=-738+814 = 76\) (incorrect)
Take \(x = 22\) (font size) and check \(y\) (word count = 114)
- For \(y=-41x + 814\): \(y=-41\times22+814=-902+814=-88\) (incorrect)
Take \(x = 24\) (font size) and check \(y\) (word count = 138)
- For \(y=-41x + 814\): \(y=-41\times24+814=-984+814=-170\) (incorrect)

Take \(x = 10\) (font size) and check \(y\) (word count = 407)
- For \(y=-26x + 723\): \(y=-26\times10+723=-260+723 = 463\) (incorrect)
Take \(x = 12\) (font size) and check \(y\) (word count = 461 or 435)
- For \(y=-26x + 723\): \(y=-26\times12+723=-312+723 = 411\) (incorrect)
Take \(x = 14\) (font size) and check \(y\) (word count = 352 or 381)
- For \(y=-26x + 723\): \(y=-26\times14+723=-364+723 = 359\) (close to 352)
Take \(x = 16\) (font size) and check \(y\) (word count = 340 or 280)
- For \(y=-26x + 723\): \(y=-26\times16+723=-416+723 = 307\) (close to 280)
Take \(x = 18\) (font size) and check \(y\) (word count = 201)
- For \(y=-26x + 723\): \(y=-26\times18+723=-468+723 = 255\) (incorrect)
Take \(x = 22\) (font size) and check \(y\) (word count = 114)
- For \(y=-26x + 723\): \(y=-26\times22+723=-572+723 = 151\) (incorrect)
Take \(x = 24\) (font size) and check \(y\) (word count = 138)
- For \(y=-26x + 723\): \(y=-26\times24+723=-624+723 = 99\) (incorrect)

Take \(x = 10\) (font size) and check \(y\) (word count = 407)
- For \(y=-38x + 922\): \(y=-38\times10+922=-380+922 = 542\) (incorrect)
Take \(x = 12\) (font size) and check \(y\) (word count = 461 or 435)
- For \(y=-38x + 922\): \(y=-38\times12+922=-456+922 = 466\) (close to 461)
Take \(x = 14\) (font size) and check \(y\) (word count = 352 or 381)
- For \(y=-38x + 922\): \(y=-38\times14+922=-532+922 = 390\) (close to 381)
Take \(x = 16\) (font size) and check \(y\) (word count = 340 or 280)
- For \(y=-38x + 922\): \(y=-38\times16+922=-608+922 = 314\) (close to 280)
Take \(x = 18\) (font size) and check \(y\) (word count = 201)
- For \(y=-38x + 922\): \(y=-38\times18+922=-684+922 = 238\) (incorrect)
Take \(x = 22\) (font size) and check \(y\) (word count = 114)
- For \(y=-38x + 922\): \(y=-38\times22+922=-836+922 = 86\) (incorrect)
Take \(x = 24\) (font size) and check \(y\) (word count = 138)
- For \(y=-38x + 922\): \(y=-38\times24+922=-912+922 = 10\) (incorrect)

Take \(x = 10\) (font size) and check \(y\) (word count = 407)
- For \(y=-55x + 407\): \(y=-55\times10+407=-550+407=-143\) (incorrect)
Take \(x = 12\) (font size) and check \(y\) (word count = 461 or 435)
- For \(y=-55x + 407\): \(y=-55\times12+407=-660+407=-253\) (incorrect)
Take \(x = 14\) (font size) and check \(y\) (word count = 352 or 381)
- For \(y=-55x + 407\): \(y=-55\times14+407=-770+407=-363\) (incorrect)
Take \(x = 16\) (font size) and check \(y\) (word count = 340 or 280)
- For \(y=-55x + 407\): \(y=-55\times16+407=-880+407=-473\) (incorrect)
Take \(x = 18\) (font size) and check \(y\) (word count = 201)
- For \(y=-55x + 407\): \(y=-55\times18+407=-990+407=-583\) (incorrect)
Take \(x = 22\) (font size) and check \(y\) (word count = 114)
- For \(y=-55x + 407\): \(y=-55\times22+407=-1210+407=-803\) (incorrect)
Take \(x = 24\) (font size) and check \(y\) (word count = 138)
- For \(y=-55x + 407\): \(y=-55\times24+407=-1320+407=-913\) (incorrect)

Answer:

\(y = - 26x+723\)