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Willow is rereading her favorite book. She starts the day on page 15. Looking at the clock, she realizes that she can read 2 pages every minute. Choose the sketch of a graph that shows the relationship between the number of minutes Willow has been reading today and the page number she is on.(1 point) which graph 1,2,3,4?

Responses

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 a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.
Image with alt text: 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 a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.

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 left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.
Image with alt text: 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 left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.

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 a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.
Image with alt text: 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 a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.

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 a plotted closed circle are left parenthesis 0 comma 2 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 6 comma 92 right parenthesis
Image with alt text: 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 a plotted closed circle are left parenthesis 0 comma 2 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 6 comma 92 right parenthesis
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1 answer

To determine which graph accurately represents the relationship between the number of minutes Willow has been reading and the page number she is on, let's analyze the information provided:

  1. Starting Page: Willow starts on page 15.
  2. Reading Speed: She reads 2 pages per minute.

This means we can calculate her page number after \( t \) minutes as follows:

  • After \( t \) minutes, her page number will be: \[ \text{Page Number} = 15 + 2t \]

For example:

  • After 0 minutes: \( 15 + 2(0) = 15 \) (which should be the starting point)
  • After 1 minute: \( 15 + 2(1) = 17 \)
  • After 2 minutes: \( 15 + 2(2) = 19 \)
  • After 10 minutes: \( 15 + 2(10) = 35 \)
  • After 30 minutes: \( 15 + 2(30) = 75 \)

Now, looking at the graph descriptions you provided:

  • Graph 1: Starts at (2, 0), which does not correspond to starting page of 15.
  • Graph 2: Starts at (0, 15), which is correct for Willow's start time and page.
  • Graph 3: Starts at (2, 0), which does not correspond to starting page of 15.
  • Graph 4: Starts at (0, 2), which does not correspond to starting page of 15.

The only graph that starts at the correct point (0, 15) and illustrates the linear progression of pages read over time, based on the formula \( \text{Page Number} = 15 + 2t \), is Graph 2.

Thus, the correct answer is Graph 2.