To determine whether the cost of pumpkins is proportional to the number bought, we will examine the relationship between the number of pumpkins and their cost. To verify proportionality, the ratios of cost to the number of pumpkins should be constant and the graph should form a straight line that passes through the origin (0,0). Here’s how we can determine this step-by-step:
1. Create a table of ratios:
| Number of Pumpkins | Cost (\$) | Ratio (Cost / Number of Pumpkins) |
|--------------------|-----------|-----------------------------------|
| 0 | 0 | Undefined (division by zero) |
| 1 | 4 | 4 / 1 = 4.0 |
| 2 | 8 | 8 / 2 = 4.0 |
| 3 | 12 | 12 / 3 = 4.0 |
| 4 | 16 | 16 / 4 = 4.0 |
We observe that the ratio for the combinations where the number of pumpkins is non-zero (1, 2, 3, 4) is consistently equal to 4.0.
2. Graph the relationship:
Let’s plot the points [tex]\((0, 0)\)[/tex], [tex]\((1, 4)\)[/tex], [tex]\((2, 8)\)[/tex], [tex]\((3, 12)\)[/tex], [tex]\((4, 16)\)[/tex] on the coordinate plane.
```
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16 |
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14 |
|
12 |
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10 |
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8 |
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6 |
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4 |
|
2 |
|
0 *---------------------------------
0 1 2 3 4
```
3. Examine the graph:
- All the plotted points [tex]\((0, 0)\)[/tex], [tex]\((1, 4)\)[/tex], [tex]\((2, 8)\)[/tex], [tex]\((3, 12)\)[/tex], [tex]\((4, 16)\)[/tex] lie on a straight line.
- This line passes through the origin [tex]\((0,0)\)[/tex].
4. Conclusion:
Since the ratio of cost to the number of pumpkins is constant (4.0), except for the case where the number of pumpkins is zero (resulting in division by zero), and the graph forms a straight line passing through the origin, we can conclude that the cost of a pumpkin is proportional to the number bought.
So, the cost of pumpkins is proportional to the number of pumpkins bought.
