Question
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 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.
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 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.
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.
Responses
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.
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 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.
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.
Answers
GPT-4o mini
To determine which graph best represents the cost of watching movies with the given pricing structure, we need to analyze the cost model:
1. There is an upfront charge of $10.
2. Each additional movie costs $2.
This means the total cost \( C \) based on the number of movies \( x \) can be described by the equation:
\[
C(x) = 10 + 2x
\]
Let's evaluate the cost for various numbers of movies:
- If \( x = 0 \):
\[
C(0) = 10 + 2(0) = 10
\]
- If \( x = 1 \):
\[
C(1) = 10 + 2(1) = 12
\]
- If \( x = 2 \):
\[
C(2) = 10 + 2(2) = 14
\]
- If \( x = 3 \):
\[
C(3) = 10 + 2(3) = 16
\]
- If \( x = 4 \):
\[
C(4) = 10 + 2(4) = 18
\]
Now let's look at the points:
- For 0 movies, cost is $10 (0, 10).
- For 1 movie, cost is $12 (1, 12).
- For 2 movies, cost is $14 (2, 14).
- For 3 movies, cost is $16 (3, 16).
- For 4 movies, cost is $18 (4, 18).
Now we check the options given:
- The **third graph** has the points:
- \( (0, 10) \)
- \( (1, 12) \)
- \( (2, 14) \)
- \( (3, 16) \)
- \( (4, 18) \)
These points match exactly with our calculated costs based on the formula \( C(x) = 10 + 2x \).
Therefore, the graph that best represents the cost of watching movies over time is the **third graph**.
1. There is an upfront charge of $10.
2. Each additional movie costs $2.
This means the total cost \( C \) based on the number of movies \( x \) can be described by the equation:
\[
C(x) = 10 + 2x
\]
Let's evaluate the cost for various numbers of movies:
- If \( x = 0 \):
\[
C(0) = 10 + 2(0) = 10
\]
- If \( x = 1 \):
\[
C(1) = 10 + 2(1) = 12
\]
- If \( x = 2 \):
\[
C(2) = 10 + 2(2) = 14
\]
- If \( x = 3 \):
\[
C(3) = 10 + 2(3) = 16
\]
- If \( x = 4 \):
\[
C(4) = 10 + 2(4) = 18
\]
Now let's look at the points:
- For 0 movies, cost is $10 (0, 10).
- For 1 movie, cost is $12 (1, 12).
- For 2 movies, cost is $14 (2, 14).
- For 3 movies, cost is $16 (3, 16).
- For 4 movies, cost is $18 (4, 18).
Now we check the options given:
- The **third graph** has the points:
- \( (0, 10) \)
- \( (1, 12) \)
- \( (2, 14) \)
- \( (3, 16) \)
- \( (4, 18) \)
These points match exactly with our calculated costs based on the formula \( C(x) = 10 + 2x \).
Therefore, the graph that best represents the cost of watching movies over time is the **third graph**.