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 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 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 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 of 10 pag

Answer 1

To interpret the slope and y-intercept from the given data, we first need to determine the slope of the linear model connecting the points on the graph.

1. Finding the slope: The slope (m) of a line can be calculated using the formula:

   \[ m = \frac{\Delta y}{\Delta x} \]

   From the data points given, let's take the points (0, 0) and (20, 210) to compute the slope.

   \[ \Delta y = 210 - 0 = 210 \] \[ \Delta x = 20 - 0 = 20 \]

   Therefore, the slope is:

   \[ m = \frac{210}{20} = 10.5 \]

   This slope indicates that for every chapter, there are approximately 10.5 pages.

2. Interpreting the y-intercept: The y-intercept is the value of y when x = 0. In this case, the point (0, 0) indicates that when there are 0 chapters, there are 0 pages. This is consistent with the interpretation that there are no pages in a nonexistent chapter.

Final interpretation:

• Slope: For every chapter of a book, there is an average of 10.5 pages.
• Y-intercept: When there are 0 chapters, there are 0 pages.

In the list of responses, the closest to our interpretation would be that for every chapter of a book, there is an average of 10 pages, but it should be noted that it should be stated as 10.5 pages, rounded accordingly.

Hence the correct interpretation of the slope is approximately:

For every chapter of a book, there is an average of 10.5 pages.