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.

For the same number of games, the member is getting gypped. S/he will be continually paying 60 units more per the same number of tokens as the nonmember.