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 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

1 answer

To determine the correct graph sketch for Willow's reading progress, we need to establish the relationship between the number of minutes she has been reading and the page number she is on.

  1. Starting Point: Willow starts on page 15.
  2. Reading Rate: She reads 2 pages every minute.

We can express the page number as a function of the minutes read (let’s denote the number of minutes as \( t \)):

  • After \( t \) minutes, the page number \( P(t) \) can be expressed as:

\[ P(t) = 15 + 2t \]

Where \( P(t) \) is the page number after \( t \) minutes, starting from page 15.

Let's evaluate some specific points:

  • At \( t = 0 \) minutes: \[ P(0) = 15 + 2(0) = 15 \]
  • At \( t = 1 \) minute: \[ P(1) = 15 + 2(1) = 17 \]
  • At \( t = 2 \) minutes: \[ P(2) = 15 + 2(2) = 19 \]
  • At \( t = 10 \) minutes: \[ P(10) = 15 + 2(10) = 35 \]
  • At \( t = 30 \) minutes: \[ P(30) = 15 + 2(30) = 75 \]

Thus, the graph should start from the point (0, 15) on the coordinate plane. As time increases, the page number will increase linearly, with a slope of 2.

Looking at the provided options, the second response describes a graph that starts at the point (0, 15) and rises to (30, 75), which aligns with our calculations.

The correct graph sketch is:

  • The second response: 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).