Question

1. is the relationship between the number of quarts picked and the weight of the strawberries proportional? explain.
2. the graph shows the number of quarts picked and the amount of money paid by different customers.

part a
what is the constant of proportionality, and what does it mean in this situation?
part b
write an equation that represents the proportional relationship shown in the graph.

Explanation:

Step1: Determine if the relationship is proportional

A proportional relationship has a graph that passes through the origin \((0,0)\). In this case, when \(x = 0\) (number of quarts \(=0\)), \(y=0\) (amount paid \(=0\)). Also, the equation of a proportional relationship is \(y = kx\), where \(k\) is the constant of proportionality.

Step2: Calculate the constant of proportionality \(k\)

Take a point \((x,y)\) from the graph. Let's assume a point \((5,7.0)\) (if we consider the general proportional - relationship formula and unit - rate calculation). The constant of proportionality \(k=\frac{y}{x}\). For example, if \(x = 3\) quarts and \(y = 4.2\) dollars (assuming a valid data - point from the context of proportionality), then \(k=\frac{4.2}{3}=1.4\).

Step3: Write the equation

Since \(y = kx\) and \(k = 1.4\), the equation representing the proportional relationship is \(y=1.4x\)

Answer:

1. Yes, the relationship is proportional because the graph passes through the origin \((0,0)\).
2. The constant of proportionality \(k = 1.4\), and it means that for each quart of strawberries picked, the customer pays \(1.4\) dollars.
3. The equation is \(y = 1.4x\)