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 straight - line graph that passes through the origin \((0,0)\). The graph in the problem passes through the origin.

Step2: Find the constant of proportionality

The constant of proportionality \(k\) (also called the unit rate) for a proportional relationship \(y = kx\) (where \(y\) is the amount paid and \(x\) is the number of quarts) can be found by taking a non - zero point \((x,y)\) on the line. Let's take the point \((2,1.2)\) (assuming from the graph's scale, if we consider \(x = 2\) and \(y=1.2\)). The formula for \(k\) is \(k=\frac{y}{x}\). So, \(k=\frac{1.2}{2}=0.6\). In general, for a proportional relationship \(y = kx\), the constant of proportionality \(k\) represents the cost per quart.

Step3: Write the equation

Using the form \(y = kx\), where \(y\) is the amount paid (in dollars) and \(x\) is the number of quarts. Since \(k = 0.6\), the equation is \(y = 0.6x\)

Answer:

1. Yes, the relationship is proportional because the graph is a straight line passing through the origin.
2. The constant of proportionality \(k = 0.6\), and it means the cost per quart of strawberries. The equation is \(y = 0.6x\)