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)

Question

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 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 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 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.
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Answer 1

To determine which graph best represents the cost of watching movies over time given the pricing structure of the movie streaming service that charges $10 up front and $2 for each movie thereafter, we can analyze how the cost changes based on the number of movies watched.

1. Cost Structure:

   • For 0 movies watched, the cost is $10 (the upfront fee).
   • For 1 movie watched: $10 + $2 × 1 = $12.
   • For 2 movies watched: $10 + $2 × 2 = $14.
   • For 3 movies watched: $10 + $2 × 3 = $16.
   • For 4 movies watched: $10 + $2 × 4 = $18.
   • This pattern continues, adding $2 for each additional movie.

2. Graph Interpretation:

   • The y-intercept (the cost when 0 movies are watched) is $10.
   • The slope of the line is $2 per movie, meaning for each additional movie, the cost increases by $2.

Based on this understanding, the graph that accurately reflects this pricing structure should start at $10 when no movies are watched and increase linearly, maintaining a slope of 2.

Now, let's analyze the provided options based on this cost pattern:

• First Graph: Starts at (0, 2) and moves up, doesn't match.
• Second Graph: Starts at (0, 10) but has decreasing points; does not match.
• Third Graph: Starts at (0, 2) and then jumps to different values; does not match.
• Fourth Graph: Starts at (0, 10) but follows a pattern that increases by 2 for each movie. Identified points (0, 10), (1, 12), (2, 14), (3, 16), (4, 18) correctly mirror the cost structure.

Thus, the fourth graph accurately represents the cost of watching movies over time according to the service's pricing model.