Question
A movie streaming service charges $10 up front and $2 for each movie thereafter. Which graph best represents the cost of watching movies over time?(1 point)
Responses
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Five unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 14 right parenthesis, left parenthesis 3 comma 16 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Five unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 14 right parenthesis, left parenthesis 3 comma 16 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 20 in increments of 2 and the y-axis labeled as dollars 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 2 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 6 comma 7 right parenthesis, left parenthesis 8 comma 6 right parenthesis, and left parenthesis 10 comma 5 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 20 in increments of 2 and the y-axis labeled as dollars 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 2 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 6 comma 7 right parenthesis, left parenthesis 8 comma 6 right parenthesis, and left parenthesis 10 comma 5 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 12 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Three unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 12 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Three unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Four unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 1 comma 3 right parenthesis, left parenthesis 2 comma 4 right parenthesis, and left parenthesis 3 comma 5 right parenthesis. A solid arrow passes through these points.
Responses
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Five unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 14 right parenthesis, left parenthesis 3 comma 16 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Five unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 14 right parenthesis, left parenthesis 3 comma 16 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 20 in increments of 2 and the y-axis labeled as dollars 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 2 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 6 comma 7 right parenthesis, left parenthesis 8 comma 6 right parenthesis, and left parenthesis 10 comma 5 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 20 in increments of 2 and the y-axis labeled as dollars 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 2 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 6 comma 7 right parenthesis, left parenthesis 8 comma 6 right parenthesis, and left parenthesis 10 comma 5 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 12 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Three unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 12 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 20 in increments of 2. Three unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 4 comma 18 right parenthesis. A solid arrow passes through these points.
A coordinate graph shows the x-axis labeled as number of movies ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 10 in 1 unit increments. Four unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 1 comma 3 right parenthesis, left parenthesis 2 comma 4 right parenthesis, and left parenthesis 3 comma 5 right parenthesis. A solid arrow passes through these points.
Answers
GPT-4o mini
To determine which graph best represents the cost of watching movies over time with the given pricing structure ($10 up front and $2 for each additional movie), we can break it down mathematically:
1. **Fixed Cost**: Initially, the cost is $10 when no movies are watched.
2. **Variable Cost**: Each additional movie costs $2.
So, the total cost can be described with the following formula:
- Total Cost (C) = $10 + $2 * (number of movies watched)
When we examine the coordinates based on this formula:
- For 0 movies: C = $10 + $2 * 0 = $10 (point: (0, 10))
- For 1 movie: C = $10 + $2 * 1 = $12 (point: (1, 12))
- For 2 movies: C = $10 + $2 * 2 = $14 (point: (2, 14))
- For 3 movies: C = $10 + $2 * 3 = $16 (point: (3, 16))
- For 4 movies: C = $10 + $2 * 4 = $18 (point: (4, 18))
Now we can verify which graph corresponds to these points:
- The first graph plots the points: (0, 10), (1, 12), (2, 14), (3, 16), and (4, 18), which perfectly matches our calculated points.
Therefore, the first graph is the correct representation of the cost of watching movies over time.
1. **Fixed Cost**: Initially, the cost is $10 when no movies are watched.
2. **Variable Cost**: Each additional movie costs $2.
So, the total cost can be described with the following formula:
- Total Cost (C) = $10 + $2 * (number of movies watched)
When we examine the coordinates based on this formula:
- For 0 movies: C = $10 + $2 * 0 = $10 (point: (0, 10))
- For 1 movie: C = $10 + $2 * 1 = $12 (point: (1, 12))
- For 2 movies: C = $10 + $2 * 2 = $14 (point: (2, 14))
- For 3 movies: C = $10 + $2 * 3 = $16 (point: (3, 16))
- For 4 movies: C = $10 + $2 * 4 = $18 (point: (4, 18))
Now we can verify which graph corresponds to these points:
- The first graph plots the points: (0, 10), (1, 12), (2, 14), (3, 16), and (4, 18), which perfectly matches our calculated points.
Therefore, the first graph is the correct representation of the cost of watching movies over time.