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.
d. create a graph of the relationship.

Explanation:

Step1: Determine the relationship type

The general form of a proportional relationship is \(y = kx\), where \(k\) is the constant of proportionality. Here, if \(x\) is time (in minutes) and \(y\) is the number of shrimp, since he cleans 4 shrimp per minute, the equation is \(y = 4x\). For a graph of \(y = 4x\), it is a straight - line passing through the origin \((0,0)\). When \(x = 0\) (no time spent), \(y=0\) (no shrimp cleaned).

Step2: Identify the unit rate

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

Step3: Write the equation

As mentioned above, using the formula for a proportional relationship \(y=kx\), with \(k = 4\) (shrimp per minute), the equation is \(y = 4x\), where \(y\) is the number of shrimp and \(x\) is the time in minutes.

Step4: Graph the relationship

To graph \(y = 4x\):

• Choose some values of \(x\). For example, when \(x = 0\), \(y = 0\); when \(x=1\), \(y = 4\); when \(x = 2\), \(y=8\).
• Plot the points \((0,0)\), \((1,4)\), \((2,8)\) on a coordinate plane. The \(x\) - axis is labeled "Time (minutes)" and the \(y\) - axis is labeled "Number of Shrimp". Then draw a straight line through these points.

Answer:

a. The relationship is proportional. The equation \(y = 4x\) is in the form \(y=kx\) (proportional relationship formula) and its graph is a straight - line passing through the origin.
b. The unit rate is 4. It means Jorge cleans 4 shrimp per minute.
c. \(y = 4x\)
d. Plot points \((0,0)\), \((1,4)\), \((2,8)\) (and more if needed) on a coordinate plane with \(x\) as time (minutes) and \(y\) as number of shrimp, then draw a straight line through them.