Question

Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4. 5, negative 3. 0, negative 1. 5, 0. 0, 1. 5. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5. 5, negative 4. 5, negative 3. 5, negative 2. 5, negative 1. 5. The second row, y, has the entries, 10, 8, 6, 4, 2. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5. 5, negative 5. 5, negative 5. 5, negative 5. 5, negative 5. 5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7. 5, negative 2. 5, 5. 0, 12. 5, 25. 0.

Answer 1

You can use the definition of a directly variating function to deduce which table represents such function.

The fourth table represents direct variation with coefficient of variation as 2.5

What is a directly variating function?

A function y = f(x) is said to be directly variating if we can write the function as: y = kx for some constant value k.

Checking all the tables to see which table is representing such function

• For first table, lets assume y = kx, then

For x = -3, y = -4.5, thus k = y/x = -4.5/-3 = -1.5

Lets check if this k is preserved for next pairs of values.

For x = -1, we will have y = 1.5 times -1 = -1.5 but y = -3 thus this table doesn't represent direct variation.

• For second table, lets assume y = kx, then

For  x = -5.5, y = 10, thus k = y/x = 10/-5.5 = -1.818..

Now for x = -4.5, y should be kx = -4.5 times -1.818.. = 8.18.. but given y is 8. Thus this table doesn't represent direct variation.

• For third table, lets assume y = kx, then

For x = -5.5, there are many values of y. But since k is assumed constant and x = -5.5 is also a constant thus y should be a unique constant and is not supposed to have multiple values as shown in table, thus it doesn't represent direct variation.

Actually, this isn't a function either since for one input, a function always outputs only one output.

• For fourth table, lets assume y = kx, then

For x -3, y = -7.5, thus k = y/x = -7.5/-3 = 2.5

Now for rest of the values of x, we expect these values:

$x = -1, y = kx = 2.5 \times -1 = -2.5\\\\ x = 2, y = kx = 2.5 \times 2 = 5.0\\\\ x = 5, y= kx = 2.5 \times 5 = 1.25\\\\ x = 10, y= kx = 2.5 \times 10 = 25.0$

Since given y values are same as we obtained, thus, this table represents direct variation with factor 2.5

Thus, fourth table represents direct variation with coefficient of variation as 2.5

Learn more about direct variation function here:

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