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 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 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 10 chapters of a book, there is an average of 1 page.
The correct response is:
For every chapter of a book, there is an average of 10 pages.
The slope of the linear model can be interpreted as the average number of pages per chapter. From the given graph, we can see that the line passes through the point (0, 0) and (17, 170).
Using these two points, we can calculate the slope by taking the change in y-coordinates (change in pages) divided by the change in x-coordinates (change in chapters).
Change in y-coordinates: 170 - 0 = 170
Change in x-coordinates: 17 - 0 = 17
Slope = Change in y-coordinates / Change in x-coordinates
= 170 / 17
= 10
Therefore, the slope of the linear model is 10. This means that, on average, there are 10 pages per chapter in the book.
The y-intercept of the linear model can be interpreted as the starting point for the number of pages when there are no chapters. From the graph, the y-intercept is (0, 0). This means that when there are no chapters (x = 0), there are no pages (y = 0).
Therefore, the y-intercept of the linear model is 0.
In conclusion, the slope of the linear model is 10, indicating that there are, on average, 10 pages per chapter. The y-intercept is 0, indicating that when there are no chapters, there are no pages.
To answer this question, we need to analyze the given information in the illustration.
The upward slanting line that starts at the point (0, 0) and continues to the point (17, 170) represents a linear model. This line represents the relationship between the number of chapters and the number of pages in a book.
The slope of the line represents the rate of change, or how much the number of pages increases for each additional chapter. To find the slope, we can use the formula:
slope = change in y / change in x
In this case, the change in y (pages) is 170 - 0 = 170, and the change in x (chapters) is 17 - 0 = 17.
Therefore, the slope is:
slope = 170 / 17 = 10
The slope of the linear model is 10, which means that for every chapter of a book, there is an average of 10 pages.
Now let's analyze the y-intercept. The y-intercept is the point where the line intersects the y-axis, and it represents the value of y (pages) when x (chapters) is 0.
From the illustration, we can see that the y-intercept is at the point (0, 0). Therefore, when x (chapters) is 0, y (pages) is also 0.
So, the y-intercept of the linear model is 0.
In summary, the slope of the linear model is 10, which means that for every chapter of a book, there is an average of 10 pages. The y-intercept is 0, indicating that when there are no chapters (x=0), there are no pages (y=0).