Question

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: Understand the concept of constant of proportionality

In a proportional relationship \(y = kx\), \(k\) is the constant of proportionality. Here, \(y\) is the amount paid and \(x\) is the number of quarts.

Step2: Calculate the constant of proportionality

From the graph (assuming a point \((x,y)\) like \((1,0.6)\) - since when \(x = 1\) (1 quart), if \(y=0.6\) (amount paid $0.6$). Using the formula \(k=\frac{y}{x}\), substituting \(x = 1\) and \(y=0.6\), we get \(k=\frac{0.6}{1}=0.6\).

Step3: Write the proportional equation

Using the form \(y = kx\), with \(k = 0.6\), the equation is \(y=0.6x\)

Answer:

The constant of proportionality is \(0.6\) and it means the cost per quart. The equation is \(y = 0.6x\)