The yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = x + 60 for a member and y = x for a nonmember. Explain how the graph of a nonmember’s yearly cost will differ from the graph of a member’s yearly cost.
The equation y = x + 60 represents the yearly cost for a member of the video game arcade. This equation indicates that the cost for a member is determined by the number of game tokens purchased (x) plus a fixed additional cost of $60.
On the other hand, the equation y = x represents the yearly cost for a nonmember of the arcade. For a nonmember, their yearly cost is solely based on the number of game tokens purchased, with no additional fixed cost.
In terms of the graphs, the graph for a member's yearly cost will be a straight line that starts at $60 (the y-intercept) and rises at a slope of 1 (indicating that for each additional game token purchased, the cost increases by $1).
In contrast, the graph for a nonmember's yearly cost will also be a straight line but without any y-intercept or additional fixed cost. This means that the graph will start at the origin (0,0) and rise at a slope of 1 (indicating that for each additional game token purchased, the cost increases by $1).
In summary, the difference between the graphs lies in the presence or absence of a fixed additional cost for members and nonmembers of the arcade.
To understand how the graphs of a nonmember's yearly cost and a member's yearly cost differ, we need to analyze the given equations.
For a member, the yearly cost is represented by the equation y = x + 60. This equation implies that a $60 fee is added to the total cost of tokens, regardless of the number of tokens purchased. Hence, the graph of a member's yearly cost will be a straight line that starts at 60 on the y-axis (representing the fixed cost) and has a slope of 1 (representing the variable cost per token).
On the other hand, for a nonmember, the yearly cost is given by the equation y = x. In this case, there is no fixed fee, as only the total cost of tokens is considered. So, the graph of a nonmember's yearly cost will be a straight line passing through the origin (0,0) with a slope of 1, indicating that the cost increases proportionally with the number of tokens purchased.
In summary, the difference between the graphs of a member's yearly cost and a nonmember's yearly cost is that the member's graph will have a positive y-intercept at 60, representing the fixed fee, while the nonmember's graph will pass through the origin (0,0), indicating no fixed fee.