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

Answer:

Fill in the blank with 14

Step-by-step 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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

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

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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{6 - 2}{2 - 1}$

$m = \frac{4}{1}$

$m=4$

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 $y = 4x -2$

$y = 4 * 4 - 2$

$y = 16 - 2$

$y = 14$