The graph below shows the relationship between the side length in feet of a square piece of carpet and its price in dollars. If s is the side length and p is the price, which of these equations does the graph represent?

Question

(1 point)
Responses

p=2.5s2
p is equal to 2 point 5 s squared

p=10s
p is equal to 10 s

p=s2
p is equal to s squared

p=5s

Answer 1

To determine which equation best represents the relationship between the side length \( s \) of the square carpet and its price \( p \), we need to consider how the price relates to the area of the carpet.

Since the area \( A \) of a square is given by \( A = s^2 \), and if the price is proportional to the area, we would expect the price to relate to the side length via an equation like \( p = k s^2 \), where \( k \) is a constant representing the price per square foot.

Now let's analyze the options given:

1. \( p = 2.5s^2 \): This suggests that the price is proportional to the area, which is a reasonable assumption for carpet pricing.

2. \( p = 10s \): This implies a linear relationship between price and side length, suggesting price increases linearly with the side length, not considering the area.

3. \( p = s^2 \): This would also imply that the price is directly equal to the area, but without a proportional factor necessarily aligning with reality.

4. \( p = 5s \): Similar to option 2, this suggests a linear relationship.

Given that carpet pricing is typically based on area, the most plausible equation from the graph would be \( p = 2.5s^2 \), as it captures the proportional relationship between price and area effectively.

Therefore, the correct option is:

\( p = 2.5s^2 \)