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
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (1,2)[/tex]
[tex](x_2,y_2) = (2,6)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6 - 2}{2 - 1}[/tex]
[tex]m = \frac{4}{1}[/tex]
[tex]m=4[/tex]
The equation of the table is calculated next as:
[tex]y - y_1 = m(x - x_1)[/tex]
This becomes
[tex]y - 2 = 4(x - 1)[/tex]
[tex]y - 2 = 4x - 4[/tex]
Solve for y
[tex]y = 4x - 4+2[/tex]
[tex]y = 4x -2[/tex]
To fill in the blank;
The value of x is 4
So, substitute 4 for x in [tex]y = 4x -2[/tex]
[tex]y = 4 * 4 - 2[/tex]
[tex]y = 16 - 2[/tex]
[tex]y = 14[/tex]
