Question

at a local farm, customers pick their own strawberries using quart or half - quart. the table shows the amounts picked by three customers. weights are rounded to the nearest tenth of a pound.

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.

1. another customer pays $8.75 for the strawberries she picks. what point $(x,y)$ on the graph shown in question 2 represents this?

Explanation:

Step1: Find the constant of proportionality

For a proportional relationship \(y = kx\), \(k=\frac{y}{x}\). From the graph, when \(x = 1\), \(y = 1.4\). So \(k=\frac{1.4}{1}=1.4\). It means the cost per quart of strawberries.

Step2: Write the equation

Using the formula \(y = kx\) with \(k = 1.4\), the equation is \(y=1.4x\).

Step3: Find the point \((x,y)\)

We know \(y = 8.75\) and \(y=1.4x\). Then \(x=\frac{y}{1.4}=\frac{8.75}{1.4}=6.25\). So the point is \((6.25,8.75)\)

Answer:

Part A: The constant of proportionality \(k = 1.4\), it means the cost per quart of strawberries.
Part B: \(y = 1.4x\)

1. \((6.25,8.75)\)