Question

use the table to determine whether the relationship is proportional. if so, write an equation for the relationship. Tell what each variable you use represents.

Answer 1

Answer:

1) a. Yes, b. $y=27*x$, c. Number of tickets= x, d. Total cost = y.

2) a. Yes b. $y=4.35x$, c. Weight = x,  d. Total cost = y.

Step-by-step explanation:

Since we know that directly proportional equations are in form of $y=k*x$, where k is proportionality constant.

1. Let x be the number of tickets and y be the total cost.

Upon looking at our first table we can see that the relationship between number of tickets and their cost is directly proportional.

We can write this relationship as $y=27*x$. 27 is our constant of proportionality. We can find it by subtracting cost of 2 tickets from cost of 3 tickets as $81-54=27$. We can see that this is true for any two consecutive values on our table. (108-81), (135-108)

2. Let x be weight and y be total cost.

We can see that data values on second table also represent proportional relationship. We can represent this relationship as $y=4.35x$

We can see that cost difference of weights for 5th and 4th value is $21.75-17.40=4.35$

Now let us verify it by finding the cost difference between weights 46 and 5

$\frac{200.10-21.75}{46-5} =\frac{178.35}{41} =4.35$

Therefore, our both table data value represent proportional relationships.