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.
c. write an equation that determines the number of shrimp cleaned given any time.

Explanation:

Step1: Determine if the relationship is proportional

A proportional relationship has the form \(y = kx\), where \(k\) is a constant. Let \(x\) be the time (in minutes) and \(y\) be the number of shrimp. Since he cleans 4 shrimp per minute, the equation is \(y = 4x\). 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 \(=0\)). So, the relationship is proportional.

Step2: Find the unit rate

The unit rate is the coefficient of \(x\) in the equation \(y = kx\). Here, \(k = 4\). In the context of the situation, the unit rate of 4 means that Jorge cleans 4 shrimp per 1 minute.

Step3: Write the equation for the number of shrimp cleaned

We know that the number of shrimp \(y\) is related to the time \(x\) (in minutes) by the formula \(y=4x\), where 4 is the rate at which he cleans shrimp (shrimp per minute).

Answer:

a. The relationship is proportional. The equation is \(y = 4x\) (a straight - line through the origin on a graph).
b. The unit rate is 4. It means Jorge cleans 4 shrimp per minute.
c. The equation is \(y = 4x\), where \(y\) is the number of shrimp and \(x\) is the time in minutes.