Question

It says to find the rule on this question but I need help finding the rule.

Answer 1

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:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

In the table:

x₁ = 8, y₁ = 10, x₂ = 9, y₂ = 12

`\begin{gathered} m\text{ = }(12-10)/(9-8) \\ m\text{ = }(2)/(1) \\ m\text{ =2 } \end{gathered}`

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

`y-y_1=m(x-x_1)`
`\begin{gathered} y\text{ - 10 = 2(x - 8)} \\ y\text{ - 10 = 2x - 16} \\ y\text{ = 2x - 16 + 10} \\ y\text{ = 2x - 6} \end{gathered}`

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