Answer:
(a) To sketch the graph representing the situation, we can use a coordinate plane with one axis representing the number of bags of popcorn and the other axis representing the number of drinks.
Let's label the x-axis as the number of bags of popcorn and the y-axis as the number of drinks.
The price for each bag of popcorn is $5, and the price of each drink is $3.
To find the intercepts, we can set up equations using the given information:
When there are no bags of popcorn, the cost of drinks would be $30. This gives us the point (0, 10) on the y-axis.
When there are no drinks, the cost of bags of popcorn would be $30. This gives us the point (6, 0) on the x-axis.
(b) The graph represents the different combinations of bags of popcorn and drinks that Judy can buy with her $30. Each point on the graph represents a specific combination of bags of popcorn and drinks that would cost a total of $30.
The line connecting the two intercepts represents all the possible combinations of bags of popcorn and drinks that Judy can buy with her $30. Any point on this line would satisfy the equation:
5(x) + 3(y) = 30
where x represents the number of bags of popcorn and y represents the number of drinks.
For example, the point (3, 5) on the line represents the combination of 3 bags of popcorn and 5 drinks, which would cost a total of $30:
5(3) + 3(5) = 15 + 15 = 30
Similarly, any point below the line would represent combinations that cost less than $30, and any point above the line would represent combinations that cost more than $30.
By sketching the graph and labeling the intercepts, we can visually represent the possible combinations of bags of popcorn and drinks that Judy can buy within her budget of $30.