To determine the correct graph, we start with the information given:
- Willow starts on page 15.
- She reads 2 pages every minute.
Now, let's create a relationship between time (in minutes) and the page number:
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At time \( t = 0 \) minutes, she is on page 15.
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After 1 minute, she will be on page \( 15 + 2 = 17 \).
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After 2 minutes, she will be on page \( 15 + 4 = 19 \).
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After 3 minutes, she will be on page \( 15 + 6 = 21 \).
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Continuing this way, after \( t \) minutes, the page number can be expressed as:
\[ \text{Page number} = 15 + 2t \]
Now we identify the graph characteristics based on this equation:
- The y-intercept (when \( t = 0 \)) is 15, so the plotted closed circle should be at \( (0, 15) \).
- The slope of the line is 2, which means for every 1 minute, the page number increases by 2 pages.
From the choices provided, we look for a graph where:
- There is a closed circle at \( (0, 15) \).
- The line representing the relationship should go up from that point, increasing by 2 pages for each minute.
The correct graph is:
"A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of the plotted closed circle are \( (0, 15) \). An upward slanting arrow extends from the plotted point and passes through \( (30, 75) \)."
This graph correctly reflects the relationship between minutes read and the page number reached.