John has a job that requires him to travel 3 of every 4 weeks. He has an annual budget and can travel either by train or by plaine. The airline on which he typically flies has a frequent traveler programme that reduces the cost of his tickets according to the number of milels he has flown in a given year. When he reaches 25000 kilometres, the airline will reduce the price of ticket by 25 percent for the remainder of the year. When he reaches 50000 kilometres, the airline will reduce the price by 50 percent for the remainder of the year. Graphically illustrate john's budget line, with train kilometres on the vertical axis and plane kilometres on the horizontal axis.

To graphically illustrate John's budget line, we need to plot the combinations of train and plane kilometers that he can afford given his annual budget.

Let's start by labeling the axes. We will put train kilometers on the vertical axis and plane kilometers on the horizontal axis.

Next, we need to determine John's budget constraints. We know that he travels 3 out of every 4 weeks, so he will have 13 weeks of travel in a year. Let's assume that his annual budget allows him to travel a total of 39 weeks (3 weeks per month for 13 months).

To create the budget line, we will plot two points: one point where John spends his entire budget on plane travel, and another point where he spends his entire budget on train travel.

1. Plane travel point:
- Let's assume that John's annual budget allows him to travel a maximum of 39 * 50000 = 1,950,000 plane kilometers.
- Since he travels 3 out of 4 weeks, he will have a total of 39 * 3 = 117 weeks of plane travel.
- Therefore, the point on the graph will be (1,950,000, 117).

2. Train travel point:
- The remaining budget after spending it all on plane travel will be the budget available for train travel.
- Let's calculate the remaining budget using the formula: remaining budget = total budget - (spent on plane travel/2)
- The remaining budget will be: 1,950,000 - (1,950,000/2) = 1,950,000 - 975,000 = 975,000 train kilometers.
- The total number of weeks he can travel by train will be: 39 - 117 = -78 (negative because he has already used more than the total budget).
- Therefore, the train travel point on the graph will be (975,000, -78).

Now, plot these two points on the graph and draw a straight line connecting them. This line represents John's budget line, showing all the combinations of train and plane kilometers that he can afford within his budget.

Please note that the negative value for train kilometers is used just for the purpose of illustrating the budget line and may not have a practical interpretation.