Question

Help plz (please don’t answer saying A or B. That answer makes 0 sense...stop) thx

Answer 1

Hey there! :D

Think of it this way. The question is saying that the text messages are all equally the same value, or expense. If you were to divide 16 by $3.20, you would find that each text was the same amount to send. That the input (the number of text messages) is directly related in the same pattern to the output (the cost of the text messages). 

A. What is the constant of proportionality in this proportional relationship? 

A constant of proportionality is what makes x directly relate in proportion to y.  We are trying to find the variable that makes y= (?)x

16y= 3.20x

Divide both sides by 16. 

y=0.20x or y=0.2x 

The constant is the value that goes with the variable. .20 is the constant. '

B. Write an equation to represent this proportional relationship. Make sure to define the variables you use. 

We already know that 0.20 is the constant number. In other words, every text message cost $.20. 

Text messages= T cost= C

C= T(0.20) 

For every text message (T), it is multiplied by 0.20, to make the accurate cost (C). 

I hope this helps!
~kaikers

Answer 2

The general equation for a direct proportion is

$y = kx$

where $k$ is the constant of proportionality.

If you have just one single (x, y) point of the relation given, you can plug in the values of x and y and solve for k. Once you know k, you write again y = kx, using the actual value of k, and that is the equation of the direct relation.

Naomi's cell phone plan is a direct proportion.
The cost in dollars varies directly with the number of texts.

That allows us to write the general equation of this relation as

y = kx

where is y is cost in dollars, x is the number of texts, and k is the constant of proportionality.

Now we use the given point to find the value of k, the constant of proportionality.

We are told that 16 texts cost $3.20. We have the (x, y) point (16, 3.2).

y = kx

3.2 = k * 16

Divide both sides by 16 to get

k = 3.2/16

k = 0.2

The constant of proportionality is 0.2

Now that we know the constant of proportionality, we just replace k with it, and we have the equation of our relationship.

y = 0.2x

where y = cost of the texts in dollars, and
x = number of texts