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.

Question

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

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 based on the data provided, we first need to determine the slope of the line.

The slope (m) is calculated as the change in the y-axis divided by the change in the x-axis, which can be expressed mathematically as:

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

From the points given, let's take two known points for this calculation: (0, 0) and (17, 170).

• For (0, 0), the value of y (pages) is 0 when x (chapters) is 0.
• For (17, 170), the value of y is 170 when x is 17.

Now we calculate the change in y and change in x:

• Change in y = 170 - 0 = 170
• Change in x = 17 - 0 = 17

Now we can calculate the slope:

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

This means that for every 1 chapter of a book, there is an average of 10 pages.

The y-intercept (b) is the value of y when x = 0. In this case, when there are 0 chapters, there are 0 pages, so the y-intercept is 0.

Thus, the slope and y-intercept can be interpreted as:

• Slope (m): For every chapter of a book, there is an average of 10 pages.
• Y-Intercept (b): When there are 0 chapters, there are 0 pages.

Given the responses provided, the correct interpretation would be: For every chapter of a book, there is an average of 10 pages.