To model the situation where Mrs. Harris spends $10 per ticket and $5 per bucket of popcorn with a total budget of $50, we can create a linear equation. We define variables: let x be the number of tickets and y be the number of buckets of popcorn. The total cost can be expressed as 10x (for tickets) plus 5y (for popcorn). Since she wants to spend no more than $50, we set up the equation 10x + 5y = 50. This equation is in standard form, which is typically written as Ax + By = C, where A, B, and C are constants. In this case, A is 10, B is 5, and C is 50. The slope-intercept form, on the other hand, is typically written as y = mx + b, which is not the format we derived here.