Answer:
y = 2x - 6
n = 22
Explanations:
By careful observation of the data in the table, the table has a constant rate of change, that is, a constant slope, hence it represents a staight line
The slope is calculated using the formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
In the table:
x₁ = 8, y₁ = 10, x₂ = 9, y₂ = 12
[tex]\begin{gathered} m\text{ = }\frac{12-10}{9-8} \\ m\text{ = }\frac{2}{1} \\ m\text{ =2 } \end{gathered}[/tex]
Since we have confirmed that the table shows a linear equation, the equation of a line shown below can be used to form the relationship
[tex]y-y_1=m(x-x_1)[/tex][tex]\begin{gathered} y\text{ - 10 = 2(x - 8)} \\ y\text{ - 10 = 2x - 16} \\ y\text{ = 2x - 16 + 10} \\ y\text{ = 2x - 6} \end{gathered}[/tex]
The rule is therefore y = 2x - 6
To find the variable n, substitute y = n, and x = 14 into the equation y = 2x - 6
n = 2(14) - 6
n = 28 - 6
n = 22
