Question

jamie is making an essay for her college course. the scatterplot shows the relationship between the number of pages and the word count of each page. based on the data, which of these is the best prediction of the word count for a 9 - page essay? a 1600 b 1800 c 2100 d 7000

Explanation:

Step1: Analyze the scatter plot trend

The scatter plot shows a positive linear relationship between the number of pages (x - axis) and word count (y - axis). As the number of pages increases, the word count generally increases. We can estimate the slope of the line of best fit. Let's take two points, for example, when \(x = 1\), \(y\approx200\); when \(x = 2\), \(y\approx400\); when \(x = 3\), \(y\approx800\)? Wait, no, looking at the grid, let's check the coordinates. Let's list some points: (1, 200), (2, 400), (3, 800)? No, wait the y - axis is word count: 0, 200, 400, 600, 800, 1000, 1200, 1400, 1500, 1800, 2000. The x - axis is number of pages: 1 - 10. Let's take (1, 200), (2, 400), (3, 800)? No, maybe (1, 200), (2, 400), (3, 800) is not right. Wait, looking at the dots: at x = 1, y is around 200; x = 2, y around 400; x = 3, y around 800? No, maybe (3, 800), (4, 1000), (5, 1200), (5, 1200), (6, 1400), (7, 1800). Wait, the last dot is at x = 7, y = 1800. So the pattern: from x = 1 to x = 7, the word count increases. Let's find the rate of change. From x = 1 (200) to x = 7 (1800), the change in x is 6, change in y is 1600, so slope is \( \frac{1600}{6}\approx266.67\) per page. But maybe a better way is to see the trend. For x = 1, y≈200; x = 2, y≈400; x = 3, y≈800? No, maybe the points are (1, 200), (2, 400), (3, 800) is wrong. Wait, the y - axis labels: 0, 200, 400, 600, 800, 1000, 1200, 1400, 1500, 1800, 2000. The dots: at x = 1, y is at 200; x = 2, y at 400; x = 3, y at 800? No, maybe (3, 800), (4, 1000), (5, 1200), (5, 1200), (6, 1400), (7, 1800). So the pattern is approximately 200 words per page? Wait, no. Wait, from x = 1 (200) to x = 7 (1800), the difference in x is 6, difference in y is 1600, so per page is about 266, but when x = 7, y = 1800. Let's predict for x = 9. Let's see the trend: from x = 1 to x = 7, the word count goes from 200 to 1800. The number of pages from 1 to 7 is 6 pages, word count increase by 1600. So per page average increase: \( \frac{1800 - 200}{7 - 1}=\frac{1600}{6}\approx266.67\). So for x = 9, which is 2 pages more than x = 7 (since 9 - 7 = 2), the word count would be 1800+2*266.67≈1800 + 533.34≈2333? No, that's not one of the options. Wait, maybe I misread the points. Wait the options are 1600, 1800, 2100, 7000. Wait 7000 is too big. Let's look again. The last dot is at x = 7, y = 1800. So the trend: as x increases by 1, y increases by about 200 - 300? Wait, from x = 1 (200) to x = 2 (400): increase by 200. x = 2 (400) to x = 3 (800): increase by 400. No, that's not linear. Wait maybe the points are (1, 200), (2, 400), (3, 800), (4, 1000), (5, 1200), (5, 1200), (6, 1400), (7, 1800). So the pattern is that for each page after the first, the word count increases. Wait, maybe the line of best fit has a slope. Let's calculate the slope between (1, 200) and (7, 1800). Slope \(m=\frac{1800 - 200}{7 - 1}=\frac{1600}{6}\approx266.67\). So for x = 9, the word count would be \(y=200+(9 - 1)*266.67=200 + 2133.36\approx2333\), but that's not an option. Wait, maybe I made a mistake. Wait the options are A.1600, B.1800, C.2100, D.7000. D is too big. Let's look at the trend again. At x = 7, y = 1800. So for x = 9, which is 2 pages more than x = 7, if we assume a linear trend, from x = 1 to x = 7, 6 pages, 1600 word increase. From x = 7 to x = 9, 2 pages, so word increase would be \( \frac{1600}{6}*2\approx533\), so 1800 + 533≈2333, but the closest option is C.2100? Wait, maybe the points are (1, 200), (2, 400), (3, 800) is wrong. Wait, maybe the y - axis is 0, 200, 400, 600, 800, 1000, 1200, 1400, 1500, 1800, 2000. The dots: at x = 1, y = 200; x = 2, y = 400; x = 3, y = 800; x = 4, y = 1000; x = 5, y = 1200; x = 5, y = 1200; x = 6, y = 1400; x = 7, y = 1800. So the pattern is that the word count is approximately 200 per page for the first two pages, then more? No, maybe the line of best fit is a linear regression. Let's use two points: (3, 800) and (7, 1800). Slope \(m=\frac{1800 - 800}{7 - 3}=\frac{1000}{4}=250\). So the equation is \(y - 800 = 250(x - 3)\), so \(y=250x - 750 + 800=250x + 50\). For x = 9, \(y=250*9+50=2250 + 50=2300\), which is close to 2100? Wait, maybe another pair of points. (5, 1200) and (7, 1800). Slope \(m=\frac{1800 - 1200}{7 - 5}=\frac{600}{2}=300\). Equation: \(y - 1200 = 300(x - 5)\), \(y=300x - 1500 + 1200=300x - 300\). For x = 9, \(y=300*9 - 300=2700 - 300=2400\), still not matching. Wait, maybe the question is about the trend, and the options: D is 7000, which is way too big. A is 1600, B is 1800 (which is at x = 7), C is 2100, D is 7000. Since the number of pages is 9, which is more than 7, the word count should be more than 1800. So between 2100 and 7000, 7000 is too big, so 2100 is a better prediction.

Step2: Eliminate incorrect options

- Option A (1600): Less than the word count at 7 pages (1800), so incorrect as 9 pages should have more words.
- Option B (1800): Word count at 7 pages, 9 pages should have more, so incorrect.
- Option D (7000): Way too large, not in line with the trend.
- Option C (2100): More than 1800 and reasonable based on the increasing trend.

Answer:

C. 2100