Final answer:
The equation 2x + 4y = 12, when graphed, intercepts the y-axis at y=3, indicating that the maximum number of boxes of tea you can buy is 3 if you spend nothing on coffee.
Step-by-step explanation:
To graph the equation 2x + 4y = 12 on a coordinate plane, we first want to find where the line of the equation would intercept the axes, which are the points when either x or y equals zero. Thus, when x=0 (no bags of coffee), 4y=12, which simplifies to y=3. This is our y-intercept, which indicates the maximum number of boxes of tea you can buy is 3, because no budget remains for coffee. Conversely, when y=0 (no boxes of tea), 2x=12, which simplifies to x=6. This is our x-intercept, representing the maximum number of bags of coffee you can buy. Thus, to draw the line, plot the points (0, 3) and (6, 0) on the graph and join them with a straight line.
The maximum number of boxes of tea you can buy without spending any money on coffee is when x=0, which we have already calculated as 3 boxes of tea (option 2). Therefore, that's the correct answer to the problem given.