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Question

An illustration shows the first quadrant of a coordinate plane titled Chapters of a Books versus pages. The x-axis shows chapters and ranges from 0 to 20 in increments of 1. The y-axis shows pages and ranges from 0 to 220 in increments of 20.
Ten points are plotted on the graph. The points are plotted at approximate coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma 20 right parenthesis, left parenthesis 4 comma 45 right parenthesis, left parenthesis 5 comma 50 right parenthesis, left parenthesis 8 comma 95 right parenthesis, left parenthesis 10 comma 90 right parenthesis, left parenthesis 12 comma 130 right parenthesis, left parenthesis 17 comma 170 right parenthesis, left parenthesis 18 comma 160 right parenthesis, and left parenthesis 20 comma 210 right parenthesis. An upward slanting line starts at left parenthesis 0 comma 0 right parenthesis and continues to left parenthesis 17 comma 170 right parenthesis.

A librarian collected data on the number of pages in chapters of a book. Interpret the slope and the y
-intercept of the linear model. Round the slope to the nearest hundredth.

(1 point)
Responses

For every 10 chapters of a book, there is an average of 1 page.
For every 10 chapters of a book, there is an average of 1 page.

For every chapter of a book, there is an average of 10 pages.
For every chapter of a book, there is an average of 10 pages.

For every chapter of a book, there is an average of 0.1 page.
For every chapter of a book, there is an average of 0.1 page.

For every chapter of a book, there is an average of110
page.
For every chapter of a book, there is an average of Start Fraction 1 over 10 End Fraction page.
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Answer 1

To find the slope and y-intercept of the linear model based on the given points,

1. Calculate the Slope: The slope (m) is calculated by taking the change in y (pages) and dividing it by the change in x (chapters).

From the points provided, we can use the points (0, 0) and (17, 170) to find the slope:

\[ m = \frac{\Delta y}{\Delta x} = \frac{170 - 0}{17 - 0} = \frac{170}{17} = 10 \]

So, the slope rounded to the nearest hundredth is 10.00.

2. Interpret the Slope: The slope of 10 indicates that for every chapter of a book, there is an average of 10 pages.

3. Determine the Y-Intercept: The y-intercept (b) is the value of y when x = 0. From the point (0, 0), we see that when there are 0 chapters, there are 0 pages, which means the y-intercept is 0.

Conclusion:

• Slope Interpretation: For every chapter of a book, there is an average of 10 pages.
• Y-Intercept: The y-intercept is 0, indicating that when there are no chapters, there are no pages.

Thus, the correct response is:

For every chapter of a book, there is an average of 10 pages.