Final answer:
To sketch the graph that represents the situation, use the number of bags of popcorn as the x-axis and the number of boxes of candy as the y-axis. The intercepts represent the points where one variable is zero.
Step-by-step explanation:
To sketch the graph that represents the situation, we can use the number of bags of popcorn as the x-axis and the number of boxes of candy as the y-axis. The intercepts represent the points where one variable is zero. Since the price of each bag of popcorn is $9, when Megan buys zero bags of popcorn, she will have $45 left to spend on candy. Therefore, the y-intercept is at (0, 45). On the other hand, the price of each box of candy is half the price of a bag of popcorn, so when Megan buys zero boxes of candy, she will have $45 to spend on popcorn. Therefore, the x-intercept is at (5, 0).
The graph would be a straight line that starts at the y-intercept (0, 45) and passes through the x-intercept (5, 0). This line represents all the possible combinations of bags of popcorn and boxes of candy that Megan can buy while spending exactly $45.