Question

28910Which table of ordered pairs represents a proportional relationship?х-34-5y321Х-1-3-5y135х-2.-4-6у-5-7-9y0-2.I need help.

Answer 1

If we follow that two quantities are proportional, they need to be multiplied by a factor. If they are directly proportional, the value is a factor that multiplies the relationship. If they are inversely proportional, the value is a reciprocal factor that multiplies this relationship. This factor must be the same for the relationship.

Then, we have that the only factor is:

x y

-1 1

-3 3

-5 5

Since we have that

`(y)/(x)=(1)/(-1)=(3)/(-3)=(5)/(-5)=-1`

The factor is constant, it is the same for all the values. Then, this table, the second one, represents a proportional relationship (the second option):

x y

-1 1

-3 3

-5 5

The other tables represent different relationships or proportions between the variables (following the same procedure):

The first option has different values for the relationship of y/x = (-1, -1/2, -1/5), the third has (5/2, 7/4, 3/2), and the last one (0, 1/3, 1/2). The second table gives us a unique value for the relationship between the variables y/x = (-1, -1, -1).