Use the image to answer the question.

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 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.

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

Answer 1

To interpret the slope and y-intercept of the linear model, let's first gather the required information from the provided points and descriptions.

From the points given, we can identify:

• The slope (m) of the line can be calculated by choosing two points from the graph: for instance, (0, 0) and (17, 170).

Using the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in our points \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (17, 170)\):

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

So, the slope is 10.

This means that for every chapter of a book, there is an average of 10 pages.

The y-intercept (b) is the value of y when x = 0. From the description, when the number of chapters (x) is 0, the number of pages (y) is also 0. Therefore, the y-intercept is 0.

Given these interpretations:

• Slope: For every chapter of a book, there is an average of 10 pages.
• Y-intercept: When there are 0 chapters, there are 0 pages.

Thus, the correct response is:

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