Cherries cost ​$2​/lb. Grapes cost ​$0.50​/lb. You can spend no more than ​$2 on​ fruit, and you need at least 2 lb in all. Create a graph showing the amount of each fruit you can buy.

Answer 1

To create the graph, we can use a coordinate plane. Let the x-axis represent the pounds of cherries and the y-axis represent the pounds of grapes.

Let's analyze the given information:
1. The cost of cherries is $2 per pound.
2. The cost of grapes is $0.50 per pound.
3. The maximum budget is $2.
4. The minimum requirement is 2 pounds of fruit.

To fulfill the minimum requirement of 2 pounds, we can either buy 2 pounds of cherries or 2 pounds of grapes. For the maximum budget of $2, we can spend all the money on grapes since they are cheaper.

Therefore, the graph will include the following points:

(2, 0) --> Represents buying 2 pounds of cherries and 0 pounds of grapes.
(0, 4) --> Represents buying 0 pounds of cherries and 4 pounds of grapes.

To illustrate the graph accurately, we need to determine the axis' scale. Since the minimum requirement for both fruits is 2 pounds, we will set the minimum value for both axes at 0. On the x-axis (cherries), we can set a maximum value of, for example, 4 pounds. On the y-axis (grapes), we can set a maximum value of 8 pounds given the constraint that spending more than $2 is not allowed.

Here is the graph:

```
8 +----------------------------------------+
| * |
7 | * |
| * |
6 | * |
| * |
5 | * |
| * |
4 | * + |
| +* | |
3 | | * |
| | |
2 |* | |
|----------------------------------------+
0 2 4 6
Cherries (lb)
```

Please note that the grapes' weights are not explicitly marked on the graph, but the diagonal line represents a range of possible weights (from 0 to 4 pounds). The shaded area above the line represents the combinations of cherries and grapes that satisfy both the budget and weight constraints.