Which of the following correctly describes the x-intercept?
Understand the Problem
The question is asking about the x-intercept in a graphical representation of pages left to read versus hours. The x-intercept represents the point at which the reading is completed, meaning no pages are left to read. The answer choices provide different interpretations of this point.
Answer
The book is 320 pages.
Answer for screen readers
The book is 320 pages.
Steps to Solve
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Identify the x-intercept
To find the x-intercept on the graph, we look for the point where the line crosses the x-axis. At this point, the number of pages left to read ( (y) ) is 0. -
Determine the value of x at the x-intercept
From the graph, the x-intercept occurs at the point where the line touches the x-axis. Here, it appears this happens at ( x = 8 ). -
Interpret the x-intercept in context
Since the x-intercept is at ( x = 8 ) hours, this means that after 8 hours of reading, the number of pages left to read ( (y) ) is 0. Hence, the answer is related to the total pages in the book, which would equal the number of pages read in those 8 hours. -
Calculate the total pages read
If there are no pages left after 8 hours, and given the slope of the line, which indicates a reading rate, we can calculate the total pages read. The slope (rate of pages read per hour) is 40 pages per hour. Thus, in 8 hours:
$$ \text{Total Pages} = \text{rate} \times \text{hours} = 40 , \text{pages/hour} \times 8 , \text{hours} = 320 , \text{pages} $$
The book is 320 pages.
More Information
The x-intercept reveals that when 8 hours are spent reading at 40 pages per hour, the entire book's 320 pages can be completed, confirming that the book totals 320 pages.
Tips
- Misinterpreting the x-intercept as the total time instead of understanding its meaning in the context of total pages read.
- Forgetting to multiply the reading rate by the number of hours to find the total pages.
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