Question

the graph shows the relationship between the number of dvds purchased, and the total cost. what is the constant of proportionality? what does it mean in this situation? the constant of proportionality is ____; it costs __ dollars per ____ dvd(s).. what does the point (4,12.80) mean in terms of the graph?

Explanation:

Step1: Find the constant of proportionality

The constant of proportionality \(k\) for a proportional relationship \(y = kx\) can be found using the formula \(k=\frac{y}{x}\).
When \(x = 2\), \(y=6.40\), then \(k=\frac{6.40}{2}=3.2\).

Step2: Interpret the constant of proportionality

The equation of the relationship is \(y = 3.2x\), where \(y\) is the cost and \(x\) is the number of DVDs. So it costs \(3.2\) dollars per \(1\) DVD.

Step3: Interpret the point \((4,12.80)\)

In the relationship \(y = 3.2x\), when \(x = 4\) (number of DVDs), \(y=12.80\) (total cost). So the point \((4,12.80)\) means that when \(4\) DVDs are purchased, the total cost is \(12.80\) dollars.

Answer:

The constant of proportionality is \(3.2\); It costs \(3.2\) dollars per \(1\) DVD(s).
The point \((4,12.80)\) means that \(4\) DVDs cost \(12.80\) dollars.