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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)

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 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

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 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.

1 answer

To determine the correct sketch for the relationship between the number of minutes Willow has been reading and the page number she is on, we need to analyze the information given.

  1. Starting Page: Willow starts on page 15.
  2. Reading Speed: She can read 2 pages every minute.

From this information, we can calculate the page number after any given number of minutes. The relationship can be expressed with the equation:

\[ \text{Page Number} = 15 + 2m \] Where \( m \) is the number of minutes read.

  • At \( m = 0 \): Page Number = 15 + 2(0) = 15
  • At \( m = 1 \): Page Number = 15 + 2(1) = 17
  • At \( m = 2 \): Page Number = 15 + 2(2) = 19
  • At \( m = 3 \): Page Number = 15 + 2(3) = 21
  • At \( m = 6 \): Page Number = 15 + 2(6) = 27
  • At \( m = 30 \): Page Number = 15 + 2(30) = 75

The start point of the graph should be \( (0, 15) \) where Willow begins reading. As the minutes increase, the page number will continue to increase with a slope indicating her reading speed.

Analyzing the Responses:

  • The second option represents the initial point as \( (0, 15) \) and shows an upward slanting arrow that is consistent with an increase in page numbers as time progresses, with mentions of passing through \( (30, 75) \), which aligns with our calculation.

Based on this information, the correct sketch of the graph is:

  • The second option: A ray extends from the plotted point \( (0, 15) \). An upward slanting arrow extends from the plotted point and passes through \( (30, 75) \).