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. 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.
B. 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.
C. 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.
The correct answer is B. 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 (0, 0); (1, -2); and (2, -4). This graph accurately represents the proportional relationship where the cost increases by $2 for every hour of internet usage.
The correct graph that shows the proportional relationship between the cost of using the internet and the time it is used is option A. It shows a line passing through three plotted points: (0, 0), (2, -1), and (4, -2). The x-axis ranges from 0 to 6 in increments of 2, and the y-axis ranges from 0 to -3 in unit decrements.
To determine which graph represents the proportional relationship between the cost and time of using the internet at the coffee shop, we can analyze the given graphs and look for the one that follows the given conditions.
The problem states that the cost for using the internet is proportional to the time it's used, and the cost is $2 per hour. This means that for every hour of internet usage, the cost increases by $2.
Looking at the graphs:
A. This graph shows a line passing through the points (0,0), (2,-1), and (4,-2). The line passes through the origin, indicating that when there is no usage, the cost is $0. Also, the points are in a straight line, implying a constant rate of change and a proportional relationship. However, the slope of the line is not equal to $2 per hour, so we can eliminate this option.
B. This graph shows a line passing through the points (0,0), (1,-2), and (2,-4). Similar to graph A, the line passes through the origin, indicating no cost for no usage. The points also form a straight line, suggesting a constant rate of change. However, the slope of the line is not $2 per hour, so we can eliminate this option as well.
C. This graph shows a line passing through the points (0,0), (2,1), (4,2), and (6,3). Again, the line passes through the origin, indicating no cost for no usage. The points are also in a straight line, suggesting a constant rate of change. Additionally, the slope of the line is $1 for every 2 hours of internet usage, which means that for every 2 hours, the cost increases by $1. However, this slope does not match the given condition of $2 per hour, so we can eliminate this option too.
After analyzing all the options, we can conclude that none of the given graphs accurately represent the proportional relationship between the cost and time of using the internet at the coffee shop.