Question

In a factory, the number of products produced by the workers on the second shift is twice the number of products produced by the first shift. Illustrate this relationship graphically. (Hint: Let x stand for the number of products produced by the first shift, and let y stand for the number of products produced by the second shift.)

Answer 1

To answer this question, we have:

1. Let x stand for the number of products produced by the first shift.

2. Let y stand for the number of products produced by the second shift.

If we have:

Then, we can write it algebraically as follows:

`y=2x`

And we can represent this relationship graphically by giving values for x, then applying the rule of the relation, and finally having the corresponding values for y.

If we suppose that workers belonging to the first shift produced:

• x = 0 products.

,

• x = 10 products.

,

• x = 20 products.

,

• x = 30 products.

,

• x = 40 products.

,

• x = 50 products.

Then, we have that the second shift will produce:

`\begin{gathered} x=10\Rightarrow y=2x\Rightarrow y=2(10)=20 \\ x=20\Rightarrow y=2(20)\Rightarrow y=40 \\ x=30\Rightarrow y=2(30)\Rightarrow y=60 \\ x=40\Rightarrow y=2(40)\Rightarrow y=80 \\ x=50\Rightarrow y=2(50)\Rightarrow y=100 \\ x=0\Rightarrow y=2(0)\Rightarrow y=0 \end{gathered}`

Therefore, we can graph the relationship using the next coordinate pairs - we can start by (0, 0) - in this case, none of the workers produced any products):

• (0, 0)

,

• (10, 20)

,

• (20, 40)

,

• (30, 60)

,

• (40, 80)

,

• (50, 100)

In this case, we can see that we are assuming that the number of products is positive integers (or natural numbers), and the relationship is discrete (not continuous) between the values for the first and second shift (that is why we do not a continuous line between the points.)

In other words, we can draw both functions for natural numbers in both axes. The y-axis will be twice in value as the values in the x-axis, and as a real ca