Mathematics: 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

4a^3b − 6a^2cStep-by-step explanation:...

Determine any data values that are missing from the

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16.03.2022

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

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