Graph Proportional Relationships Quick Check
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Question
At the coffee shop, the cost for using the internet is proportional to the time it’s used. It costs $2 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 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 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 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.
The correct graph is the one that shows a line passing through the plotted points (0, 0), (1, 2), and (2, 4). It has 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. The graph should also have a line ending with an arrow.
The correct graph to show the proportional relationship is:
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: (0, 0); (1, 2); and (2, 4).
To solve this question, we need to understand that the cost for using the internet is proportional to the time it's used. This means that as the number of hours increases, the cost will also increase at a consistent rate.
Looking at the given options, we need to select the graph that represents this proportional relationship between the number of hours (x-axis) and the cost (y-axis).
Option A describes a graph with a line passing through the points (0,0), (1,2), and (2,4). This means that when the number of hours is 0, the cost is also 0, and when the number of hours is 1, the cost is 2, and when the number of hours is 2, the cost is 4. This relationship follows the proportional relationship mentioned in the question, where the cost ($2) is equal to the number of hours multiplied by the constant rate ($2/hour). Therefore, option A represents the correct graph for the proportional relationship stated in the question.
On the other hand, options B, C, and D do not represent the given proportional relationship correctly. They either have different plotted points or do not follow the pattern of increasing cost with the increasing number of hours.
Therefore, the correct answer is the graph described in option A.