Final answer:
The question is about determining the y-intercept in a linear equation related to a budget constraint. In the example provided, Alphonso's y-intercept would be 5 burgers if he spends all his money on burgers, indicating he would have no budget left for bus tickets. Similarly, Ethan's y-intercept in his earning equation is 25, representing his base charge without hourly work.
Step-by-step explanation:
The question regarding Devon's spending and the y-intercept belongs to the subject of Mathematics, specifically to concepts of algebra and linear equations. The y-intercept is the point where the graph of a line crosses the y-axis. It represents the value of y when x is zero. In the context of a budget constraint, the y-intercept shows the maximum quantity that Devon can purchase if he spends all his money on one item with none left for other items.
Using the provided information in the reference, if Alphonso spends all his money on burgers at $2 per burger, he can afford five burgers per week, showing that the y-intercept would be 5. This is because he spends $10 per week and the price of each burger is $2, so he would not have money left for bus tickets (Point A on the graph with zero bus tickets and five burgers). Conversely, if Alphonso spends all his money on bus tickets at $0.50 each, he can afford 20 bus tickets per week, thus the x-intercept is 20 bus tickets and zero burgers (Point F).
Let's consider Ethan's case from the reference as a more detailed example: his total earnings 'y' can be represented by the linear equation y = 25 + 20x. Here, 'x' represents the independent variable, which is the number of hours of work, and 'y' represents the dependent variable, which is the total amount of money earned per visit. The y-intercept is 25, which means that Ethan has a base charge of $25 before any hourly work is performed. The slope of the line is 20, indicating that he earns $20 for each additional hour of work.