Graphing Linear Equations Unit Test

Question

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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 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.

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 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.
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Answer 1

To determine which graph best represents the cost structure of the movie streaming service, we need to analyze the pricing equation.

The cost structure is given as:

• A base fee of $10 upfront.
• An additional fee of $2 for each movie watched.

This can be represented with the following equation: \[ C(x) = 10 + 2x \] where \( C(x) \) is the total cost in dollars, and \( x \) is the number of movies watched.

With this equation:

• When \( x = 0 \) (no movies watched), the cost is \( C(0) = 10 + 2(0) = 10 \) dollars.
• When \( x = 1 \) (1 movie watched), the cost is \( C(1) = 10 + 2(1) = 12 \) dollars.
• When \( x = 2 \) (2 movies watched), the cost is \( C(2) = 10 + 2(2) = 14 \) dollars.
• When \( x = 3 \) (3 movies watched), the cost is \( C(3) = 10 + 2(3) = 16 \) dollars.
• When \( x = 4 \) (4 movies watched), the cost is \( C(4) = 10 + 2(4) = 18 \) dollars.

Thus, the key points to note are:

• At \( 0 \) movies: \( 10 \) dollars
• At \( 1 \) movie: \( 12 \) dollars
• At \( 2 \) movies: \( 14 \) dollars
• At \( 3 \) movies: \( 16 \) dollars
• At \( 4 \) movies: \( 18 \) dollars

Now, reviewing the graphs:

1. Graph Option 1 has points (0, 2), (2, 10), (4, 18) - does not match our points.
2. Graph Option 2 has points (0, 10), (1, 12), (2, 14), (3, 16), (4, 18) - matches our calculations perfectly.
3. Graph Option 3 shows decreasing cost, which is not accurate.
4. Graph Option 4 has points starting at (0, 2) which is also inaccurate.

Given this analysis, Graph Option 2 is the correct choice as it accurately represents the cost of watching movies over time based on the provided structure.