The amount of money, y, in a cash box increases as x tickets are purchased for carnival games. The slope of the line is 1/4, and the y-intercept is 8. In this context, the slope represents the rate at which money is added to the cash box per ticket sold; specifically, for each ticket sold, 1/4 of a dollar is added to the cash box. The y-intercept indicates that when no tickets are sold (x = 0), the cash box already contains 8 dollars.

The information provided describes a linear relationship between the amount of money in the cash box (y) and the number of tickets sold (x). This linear relationship can be expressed by the equation of a straight line, which in slope-intercept form is y = mx + b, where m represents the slope of the line and b represents the y-intercept.

Given that the slope (m) is 1/4 and the y-intercept (b) is 8, we can write the equation for the money in the cash box as:

y = (1/4)x + 8

This equation means that for every ticket (x) sold, 1/4 of a dollar ($0.25) is added to the cash box. When no tickets have been sold (x = 0), the cash box already contains 8 dollars. Thus, if we want to know the amount of money in the cash box after a certain number of tickets are sold, we can substitute that number in for x in the equation and solve for y.

For example, if 20 tickets are sold, the amount of money in the cash box, y, would be calculated as follows:

y = (1/4)(20) + 8 y = 5 + 8 y = 13

Thus, after selling 20 tickets, the cash box would contain 13 dollars.