Yes, $x$ and $y$ do have a proportional relationship.

Explanation:

• A proportional relationship means that the ratio between $x$ (pounds of tomatoes) and $y$ (cost in dollars) is constant. This can be represented as: $y = kx$ where $k$ is the constant of proportionality.

• In the graph:

  1. The line starts at the origin $(0, 0)$, which is a key indicator of proportionality.
  2. The line is straight, showing that the cost increases at a constant rate with the amount of tomatoes.

How to find the constant $k$:

From the graph:

• At $x = 10$ pounds, $y = 10$ dollars.
• At $x = 20$ pounds, $y = 20$ dollars, and so on.

The ratio $k$ is: $k = \frac{y}{x} = \frac{10}{10} = 1$

Thus, the cost per pound is 1 dollar, and the relationship is proportional.

Would you like further details or a breakdown of proportional relationships?

Related Questions:

1. How do you identify a proportional relationship from a table or graph?
2. What is the constant of proportionality, and how is it calculated?
3. How do you write an equation for a proportional relationship?
4. Can a graph have a straight line but not be proportional?
5. How would the graph change if the price per pound increased?

Tip:

In proportional relationships, the graph always passes through the origin (0,0) and the slope represents the constant of proportionality.