Interpreting Linear Relationships Quick Check

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Question
A scout has 100 boxes of cookies to sell. They sell 25 boxes every 3 hours. Select the graph that shows how many boxes of cookies the scout has over time.(1 point)
Responses

A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 1,000 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 1 comma 200 right parenthesis, left parenthesis 2 comma 300 right parenthesis, and left parenthesis 3 comma 400 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 1,000 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 1 comma 200 right parenthesis, left parenthesis 2 comma 300 right parenthesis, and left parenthesis 3 comma 400 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 150 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 75 right parenthesis, left parenthesis 6 comma 50 right parenthesis, and left parenthesis 9 comma 25 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 150 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 75 right parenthesis, left parenthesis 6 comma 50 right parenthesis, and left parenthesis 9 comma 25 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as hours ranging from 0 to 8 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 10 in 1 unit increments. Six unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 7 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 5 comma 5 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as hours ranging from 0 to 8 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 10 in 1 unit increments. Six unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 7 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 5 comma 5 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as hours ranging from 0 to 9 in 1 unit increments and the y-axis labeled as boxes of cookies ranging from 0 to 175 in increments of 25. Four unlabeled points are plotted as follows: left parenthesis 0 comma 100 right parenthesis, left parenthesis 3 comma 125 right parenthesis, left parenthesis 6 comma 150 right parenthesis, and left parenthesis 9 comma 175 right parenthesis. A solid arrow passes through these points.

1 answer

To determine which graph correctly represents the number of boxes of cookies the scout has over time, we need to analyze the problem statement carefully.

The scout starts with 100 boxes of cookies and sells 25 boxes every 3 hours. This means:

  • At time \( t = 0 \) hours, they have 100 boxes.
  • After 3 hours, they sell 25 boxes, so they'll have \( 100 - 25 = 75 \) boxes.
  • After 6 hours, they sell another 25 boxes, so they'll have \( 75 - 25 = 50 \) boxes.
  • After 9 hours, they sell another 25 boxes, so they'll have \( 50 - 25 = 25 \) boxes.
  • After 12 hours, they’ll sell another 25 boxes (if they had any left), leading to 0 boxes.

So, the following points can be plotted based on this information:

  • At \( t = 0 \): 100 boxes
  • At \( t = 3 \): 75 boxes
  • At \( t = 6 \): 50 boxes
  • At \( t = 9 \): 25 boxes

Now we need to see which graph shows this relationship:

  • The first graph shows points at: (0, 100), (1, 200), (2, 300), (3, 400), which do not match.
  • The second graph shows points at: (0, 100), (3, 75), (6, 50), (9, 25), which matches perfectly.
  • The third graph has incremental points decreasing by 1 every hour, which does not match.
  • The fourth graph shows points at: (0, 100), (3, 125), (6, 150), (9, 175), which does not match.

Therefore, the correct graph is the second one:

  • Points: (0, 100), (3, 75), (6, 50), (9, 25).