Bivariate Data Analysis & Probability Unit Test

Question

6 of 166 of 16 Items

Question
Use the image to answer the 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 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.
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Answer 1

To find the slope of the line representing the relationship between chapters of a book and the number of pages, we can calculate the change in the number of pages (y) with respect to the change in the number of chapters (x).

From the graph, we have two points that we can use to calculate the slope. Let’s use the endpoints of the line segment from (0, 0) to (17, 170):

• The coordinate for chapters is \( x_1 = 0 \) and \( x_2 = 17 \).
• The coordinate for pages is \( y_1 = 0 \) and \( y_2 = 170 \).

The formula for the slope \( m \) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{170 - 0}{17 - 0} = \frac{170}{17} = 10 \]

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

Next, let’s interpret the y-intercept. The y-intercept is the value of \( y \) when \( x = 0 \). From the graph, we see that the y-intercept is at the point (0, 0). This indicates that if there are 0 chapters, there are 0 pages in the book (which makes sense).

Putting this together, the interpretations are:

• The slope suggests that for every chapter of a book, there are an average of 10 pages.
• The y-intercept indicates that a book with 0 chapters does not have any pages.

Thus, the correct response based on the options provided is:

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