Final answer:
To model the situation, we can create a linear inequality where 9x + 20y ≤ 200, representing the total cost of fruit pies and cakes. The graph of the inequality is a line with a slope of -9/20 and a y-intercept of 10, where the region below the line satisfies the inequality.
Step-by-step explanation:
To create a linear inequality to model the situation, we need to define some variables. Let's say x represents the number of fruit pies and y represents the number of cakes that Jack can buy. Since fruit pies cost $9 each and cakes cost $20 each, the total amount spent on pies can be represented as 9x, and the total amount spent on cakes can be represented as 20y. The linear inequality can be expressed as 9x + 20y ≤ 200. This inequality represents that the total cost of fruit pies and cakes should be less than or equal to $200. To graph the inequality, we can rearrange it to y ≤ (-9/20)x + 10. We can then draw a line with a slope of -9/20 and a y-intercept of 10, and shade the region below the line to represent the values that satisfy the inequality.