Question

Find the value of k in the data set so that it becomes a linear function.

k = 2
k = 3
k = -2
k = -3

Answer 1

The value of k in the data set so that it becomes a linear function is k = 2.

To determine the value of k in the given data set so that it becomes a linear function, we can check the differences in the y-values for consecutive pairs of points. If the differences are constant, the data set represents a linear relationship.

Let's compute the differences in y-values:

`\Delta y_1 = 4 - 2 = 2 \]\\\Delta y_2 = 6 - 4 = 2 \]\\\Delta y_3 = 8 - 6 = 2 \]\\\Delta y_4 = 10 - 8 = 2 \]\\\Delta y_5 = 12 - 10 = 2 \]`

The differences in y are all equal to 2, indicating a constant rate of change. This confirms that the data set represents a linear function. Now, let's find k:

`\[ k = \Delta y_1 = 2 \]`

Therefore, the value of k in the data set so that it becomes a linear function is k = 2.

Complete question:

Find the value of k in the data set so that it becomes a linear function.

k = 2

k = 3

k = -2

k = -3

Data:

x y

-3 2

-2 4

-1 6

0 8

1 10

2 12