Final answer:
Keisha's profit equation for selling her artwork after accounting for the table rental cost is represented by the linear equation y = 12x - 45, where the y-intercept is -45 and the slope is 12, showing her initial cost and profit per item, respectively.
Step-by-step explanation:
To determine the equation that represents Keisha's profit y after selling x pieces of art, we can follow a similar pattern as shown in the provided examples. Keisha has a fixed cost of $45 for renting a table, which is comparable to a one-time fee. Each piece of art that she sells contributes to her earnings, much like how a service might charge an additional fee on top of a base cost in the examples provided. In the context of Keisha's situation, every piece of art sold will increase her profit by $12.
The equation for Keisha's profit will have two components: a fixed cost represented by the y-intercept and a variable component represented by the slope. The fixed cost (y-intercept) is the amount she has to pay regardless of the number of pieces sold, which is $45. The slope is the amount of money she earns per piece of art sold, which is $12. Therefore, for every piece of art she sells, her profit increases by $12.
So, her profit equation can be written as y = 12x - 45. Here, the y-intercept is -45 (since it's cost, it's considered as a negative value in terms of profit), meaning that she starts with a loss of $45 before selling any art. The slope is 12, indicating her profit per piece of art sold.