At the coffee shop, the cost for using the internet is proportional to the time it’s used. It costs $2

Question

per hour to use the internet. Select the graph drawn to show this relationship, where x represents the number of hours and y represents the cost.(1 point)
Responses

A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to negative 3 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma negative 1 right parenthesis; and left parenthesis 4 comma negative 2 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to negative 3 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma negative 1 right parenthesis; and left parenthesis 4 comma negative 2 right parenthesis.

A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to 4 in increments of 1 shows a line ending with an arrow. The line passes through 3 plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma 2 right parenthesis; and left parenthesis 2 comma 4 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to 4 in increments of 1 shows a line ending with an arrow. The line passes through 3 plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma 2 right parenthesis; and left parenthesis 2 comma 4 right parenthesis.

A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to 3 in increments of 1 shows a line ending with an arrow. The line passes through the plotted points left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 1 right parenthesis; left parenthesis 4 comma 2 right parenthesis; and left parenthesis 6 comma 3 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 6 in increments of 2 and the y-axis ranging from 0 to 3 in increments of 1 shows a line ending with an arrow. The line passes through the plotted points left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 1 right parenthesis; left parenthesis 4 comma 2 right parenthesis; and left parenthesis 6 comma 3 right parenthesis.

A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to negative 4 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to 4 in increments of 1 and the y-axis ranging from 0 to negative 4 in unit decrements shows a line ending with an arrow. The line begins at the origin and passes through three plotted points. The plotted points include left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
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Answer 1

To find the correct graph representing the relationship where the cost of using the internet is $2 per hour, we can express the relationship mathematically:

• Let \( x \) represent the number of hours.
• The cost \( y \) can be expressed as \( y = 2x \).

This means that for each hour of internet usage, the cost increases by $2.

Now, let's analyze the graphs based on the points they plot based on this equation:

1. First Graph: Passes through (0,0), (2,-1), and (4,-2). This graph does not represent the relationship, as the cost cannot be negative.

2. Second Graph: Passes through (0,0), (1,2), and (2,4). This graph represents the relationship because:

   • At 0 hours: cost = 0
   • At 1 hour: cost = $2 (correct)
   • At 2 hours: cost = $4 (correct)

3. Third Graph: Passes through (0,0), (2,1), (4,2), and (6,3). This graph incorrectly depicts the proportionality; it does not match the cost of $2 per hour.

4. Fourth Graph: Passes through (0,0), (1,-2), and (2,-4). This graph does not represent a valid cost, as costs cannot be negative.

Thus, the second graph is the correct one to represent the linear relationship where the cost of using the internet is $2 per hour.