Question

Determine any data values that are missing from the table, assuming that the data represent a linear function.

X
ly
1
2
12
16
4
a.
2
10
b.
C. 14
d. 16

Answer 1

Fill in the blank with 14

Explanation:

Given

The attached table

Required

Fill in the gap

Since, the table represents a linear function.

The first step is to calculate the slope of the table

`m = (y_2 - y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (1,2)`

`(x_2,y_2) = (2,6)`

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (6 - 2)/(2 - 1)`

`m = (4)/(1)`

`m=4`

The equation of the table is calculated next as:

`y - y_1 = m(x - x_1)`

This becomes

`y - 2 = 4(x - 1)`

`y - 2 = 4x - 4`

Solve for y

`y = 4x - 4+2`

`y = 4x -2`

To fill in the blank;

The value of x is 4

So, substitute 4 for x in
`y = 4x -2`

`y = 4 * 4 - 2`

`y = 16 - 2`

`y = 14`