(0,0), (3,20), (4,45), (5,50), (8,98), (10,90), (12,130), (17,170), (18,160), (20,210) 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.

Answer 1

To interpret the slope and y-intercept of the linear model, we need to first find the equation of the line that best fits the given data points.

Using a statistical software or calculator, we can find that the equation of the line that best fits the given data points is:

y = 8.40x + 0.28

where y represents the number of pages in a chapter and x represents the chapter number.

Interpreting the slope:
The slope of the linear model is 8.40. This means that for every increase in the chapter number by 1, the number of pages in the chapter increases by 8.40, on average.

Interpreting the y-intercept:
The y-intercept of the linear model is 0.28. This means that when the chapter number is 0 (or the start of the book), the number of pages in the chapter is 0.28, on average. However, since the number of pages in a chapter cannot be negative or a fraction, this interpretation may not be meaningful in this context. It is better to interpret the y-intercept as the starting point of the linear relationship between the chapter number and the number of pages in the chapter.

Note: The y-intercept is not always meaningful in a real-world context, but the slope can still provide valuable information about the relationship between variables.