Question

What is the interpretation of the x-intercept in the context of the problem?

1) After 1 month, the business will have $2,295 remaining for technology updates.
2) The initial technology budget for the business is $2,430.
3) The business spends $135 every month updating their technology.
4) After 18 months, the business will have $0 remaining in their technology budget.

Answer 1

The x-intercept represents the moment when the business's technology budget will be fully depleted, at the end of an 18-month period.

Step-by-step explanation:

The x-intercept in a linear equation represents the value of x when y is zero. In the context of the problem presented, where a business will have $0 remaining in their technology budget after 18 months, the x-intercept indicates the time frame at which the budget will be fully depleted. This is because the x-axis often represents time, and in this scenario, it signifies the point at which the technology budget is completely used up, correlating directly to the end of the 18-month period.

For instance, in a similar example with bus tickets and burgers taken from the reference material, if a budget constraint was graphed, the points where the line crosses the x-axis would reflect the quantity of bus tickets one could afford if they chose to purchase zero burgers. Similarly, the x-intercept of a company's budget graph would show the moment at which the budget reaches zero if one continues spending at a constant rate.