Suppose Sal’s total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich (x) and $3 for each wrap (y). In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
To understand how the graphs of the functions for sandwiches and wraps are similar and different, let's first define the functions. Let X represent the number of sandwiches and Y represent the number of wraps sold. The profit for sandwiches can be calculated using the equation P(x) = 2x, and the profit for wraps can be calculated using the equation P(y) = 3y.
Now, let's analyze the similarities between the graphs. Both graphs will be linear since the profit amounts for sandwiches and wraps are constant, with a slope of 2 for sandwiches and a slope of 3 for wraps. This indicates that for each additional sandwich sold, the profit will increase by $2, and for each additional wrap sold, the profit will increase by $3.
However, the graphs will differ in their intercepts. The intercept for sandwiches will be at (0,0), as no sandwiches sold will result in zero profit. On the other hand, the intercept for wraps will also be at (0,0), indicating that no wraps sold will also result in zero profit.
In summary, the graphs for both sandwiches and wraps will be linear with a slope of 2 and 3 respectively, but the only difference between them will be their intercepts, which are both at the origin.