Question

1. jorge is cleaning shrimp. he cleans 4 shrimp every minute. use time in minutes as the independent quantity and the number of shrimp as the dependent quantity.

a. is the relationship proportional or non - proportional? explain how you can determine this using a graph and an equation.
b. identify the unit rate of this relationship. explain what the unit rate means in terms of the situation.

Explanation:

Step1: Determine proportionality

A proportional relationship has the form \(y = kx\), where \(k\) is the constant of proportionality. Here, the number of shrimp \(y\) and time \(x\) follow \(y = 4x\) (since he cleans 4 shrimp per minute). On a graph, a proportional relationship is a straight - line passing through the origin \((0,0)\). When \(x = 0\) (time \(=0\) minutes), \(y=4\times0 = 0\) (number of shrimp \(=0\)).

Step2: Identify unit rate

The unit rate \(k\) in the equation \(y = kx\) represents the amount of the dependent variable (\(y\), number of shrimp) per one unit of the independent variable (\(x\), time). In the equation \(y = 4x\), \(k = 4\). This means that for every 1 minute (\(x = 1\)), the number of shrimp cleaned \(y=4\times1=4\). So the unit rate is 4 shrimp per minute.

Answer:

a. The relationship is proportional. The equation \(y = 4x\) is in the form \(y=kx\) (where \(k = 4\)), and on a graph, when \(x = 0\), \(y = 0\) (passes through the origin).
b. The unit rate is 4 shrimp per minute. It means that for each 1 - minute interval of time, Jorge cleans 4 shrimp.